tag:blogger.com,1999:blog-81379881368609413982018-02-14T14:55:48.928-08:00SprachlogikA philosophy blog with a focus on logic and language.Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.comBlogger133125tag:blogger.com,1999:blog-8137988136860941398.post-90907839209506048402018-01-29T22:43:00.000-08:002018-01-30T02:50:35.762-08:00Update on my Necessity and Propositions account (and my haste to declare it false)<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">In some recent posts here I have discussed propositions like 'Air is airy' (due to Jens Kipper) which we know to be necessarily true, but only because we know empirically that air is not a natural kind, and hence that all there is to being air is being airy, and 'Eminem is not taller than Marshall Mathers' (due to Strohminger and Yli-Vakkuri), which we know to be necessarily true, but only because we know empirically that Eminem <i>is</i>&nbsp;Marshall Mathers, in relation to the account of necessity defended in my <a href="https://sites.google.com/site/tristanhaze/TristanHaze-NecessityandPropositions.pdf">thesis</a>. That account says that a proposition is necessarily true iff it is in the deductive closure of the set of true inherently counterfactually invariant propositions. (Roughly, a proposition is ICI if it does not vary across counterfactual scenarios when held true. For more detail see Chapter 5 of my thesis.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">At first, I reacted by thinking that such propositions show that account to be false. I then came up with <a href="http://sprachlogik.blogspot.com/2017/09/a-new-account-of-conditions-under-which.html">another account</a>, based on the idea of a <a href="https://sprachlogik.blogspot.com.au/2017/09/the-importance-of-counterfactual.html">counterfactual invariance decider</a>. I still find this new account more elegant, but I soon came to have <a href="https://sprachlogik.blogspot.com.au/2017/11/old-account-may-not-be-false-after-all.html">doubts</a> about just how threatening they are to the ICI-based account in my thesis.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I have recently realised that the ICI-account fares even better in the face of these examples than suggested in <a href="https://sprachlogik.blogspot.com.au/2017/11/old-account-may-not-be-false-after-all.html">the post mentioned above</a>. There, I suggested in effect that 'All there is to being air is being airy' could be argued to imply 'Air is airy' on a suitably rich notion of implication, thus saving the ICI-account, and similarly that 'Eminem is Marshall Mathers' could be argued to imply 'Eminem is not taller than Marshall Mathers' on a suitably rich notion of implication.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But, I have realised, no such rich notion of implication is required! We just need to conjoin the empirical proposition which decides the modal matter with the proposition whose modal status is in question. 'Air is not a natural kind and air is airy', or 'All there is to being air is being airy and air is airy', are both true and ICI, and they both - very straightforwardly, by conjunction elimination - imply the desired proposition. For the Eminem case we have 'Eminem is Marshall Mathers and Eminem is not taller than Marshall Mathers'. So there was never a serious problem for the ICI-account after all!&nbsp;</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Admittedly, these impliers do perhaps seem a bit "clever", a bit artificial in some way, and this - together with not requiring any appeal to implication at all - is why I still think the CI decider account is more elegant.&nbsp;</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">One thing that I think went wrong in my thought process around this is that I got a kind of kick out of concluding that my original account was false. Doing so made me feel like a virtuous philosopher, open to changing their views. But I am glad that I now have a more elegant account, and the notion of a CI decider. (I wonder: Would the CI decider account still have come to me if I had not overreacted and thought my original account falsified? Or did my foolishness here cause me to come up with the CI decider account?)</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-24694206182110061302018-01-09T15:45:00.000-08:002018-01-09T15:45:05.288-08:00Robin Hanson Responds<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I recently posted <a href="http://sprachlogik.blogspot.com/2018/01/two-critical-remarks-on-elephant-in.html">criticisms</a> of Robin Hanson and Kevin Simler's excellent new social science book <i>The Elephant in the Brain. </i>Hanson responds <a href="http://www.overcomingbias.com/2018/01/elephant-in-the-brain-reviews.html">here</a>. The response is short so I will reproduce it here:</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="background-color: white; color: #353537; font-family: &quot;helvetica neue&quot;, arial, helvetica, sans-serif; font-size: 15.2px;">The&nbsp;</span><a href="http://sprachlogik.blogspot.com/2018/01/two-critical-remarks-on-elephant-in.html" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #314c85; font-family: &quot;helvetica neue&quot;, arial, helvetica, sans-serif; font-size: 15.2px; margin: 0px; padding: 0px; vertical-align: baseline;">fourth blog review</a><span style="background-color: white; color: #353537; font-family: &quot;helvetica neue&quot;, arial, helvetica, sans-serif; font-size: 15.2px;">&nbsp;was 1500 words, and is the one on a 4-rank blog, by philosopher Tristan Haze. He starts with praise:</span><br /><span style="background-color: white; color: #353537; font-family: &quot;helvetica neue&quot;, arial, helvetica, sans-serif; font-size: 15.2px;"><br /></span><div style="background: rgb(255, 255, 255); border: 0px; color: #353537; font-size: 15.2px; margin-bottom: 12px; padding: 0px 0px 0px 30px; vertical-align: baseline;"><span style="font-family: &quot;helvetica neue&quot; , &quot;arial&quot; , &quot;helvetica&quot; , sans-serif;">A fantastic synthesis of subversive social scientific insight into hidden (or less apparent) motives of human behaviour, and hidden (or less apparent) functions of institutions. Just understanding these matters is an intellectual thrill, and helpful in thinking about how the world works. Furthermore – and I didn’t sufficiently appreciate this point until reading the book, … better understanding the real function of our institutions can help us improve them and prevent us from screwing them up. Lots of reform efforts, I have been convinced (especially for the case of schooling), are likely to make a hash of things due to taking orthodox views of institutions’ functions too seriously.</span></div><div style="background: rgb(255, 255, 255); border: 0px; color: #353537; font-size: 15.2px; margin-bottom: 12px; padding: 0px; vertical-align: baseline;"><span style="font-family: &quot;helvetica neue&quot; , &quot;arial&quot; , &quot;helvetica&quot; , sans-serif;">But as you might expect from a philosopher, he has two nits to pick regarding our exact use of words.</span></div><div style="background: rgb(255, 255, 255); border: 0px; color: #353537; font-size: 15.2px; margin-bottom: 12px; padding: 0px 0px 0px 30px; vertical-align: baseline;"><span style="font-family: &quot;helvetica neue&quot; , &quot;arial&quot; , &quot;helvetica&quot; , sans-serif;">I want to point out what I think are two conceptual shortcomings in the book. …&nbsp;The authors seem to conflate the concept of common knowledge with the idea of being “out in the open” or “on the record”. … This seems wrong to me. Something may satisfy the conditions for being common knowledge, but people may still not be OK talking about it openly. … They write: ‘Common knowledge is the difference between (…) a lesbian who’s still in the closet (though everyone suspects her of being a lesbian), and one who’s open about her sexuality; between an awkward moment that everyone tries to pretend didn’t happen and one that everyone acknowledges’ (p. 55). If we stick to the proper recursive explanation of ‘common knowledge’, these claims just seem wrong.</span></div><div style="background: rgb(255, 255, 255); border: 0px; color: #353537; font-size: 15.2px; margin-bottom: 12px; padding: 0px; vertical-align: baseline;"><span style="font-family: &quot;helvetica neue&quot; , &quot;arial&quot; , &quot;helvetica&quot; , sans-serif;">We agree that the two concepts are in principle distinct. In practice the official definition of common knowledge almost never applies, though a related concept of common belief does often apply. But we claim that in practice a lack of common belief is the main reason for widely known things not being treated as “out in the open”. While the two concepts are not co-extensive, one is the main cause of the other. Tristan’s other nit:</span></div><div style="background: rgb(255, 255, 255); border: 0px; color: #353537; font-size: 15.2px; margin-bottom: 12px; padding: 0px 0px 0px 60px; vertical-align: baseline;"><span style="font-family: &quot;helvetica neue&quot; , &quot;arial&quot; , &quot;helvetica&quot; , sans-serif;">Classical decision theory has it right: there’s no value in sabotaging yourself per se. The value lies in convincing other players that you’ve sabotaged yourself. (p. 67).</span></div><div style="background: rgb(255, 255, 255); border: 0px; color: #353537; font-size: 15.2px; margin-bottom: 12px; padding: 0px 0px 0px 30px; vertical-align: baseline;"><span style="font-family: &quot;helvetica neue&quot; , &quot;arial&quot; , &quot;helvetica&quot; , sans-serif;">This fits the game of chicken example pretty well. But it doesn’t really fit the turning-your-phone-off example: what matters there is that your phone is off – it doesn’t matter if the person wanting the favour thinks that your phone malfunctioned and turned itself off, rather than you turning it off. … It doesn’t really matter how the kidnapper thinks it came about that you failed to see them – they don’t need to believe you brought the failure on yourself for the strategy to be good.</span></div><div style="background: rgb(255, 255, 255); border: 0px; color: #353537; font-size: 15.2px; margin-bottom: 12px; padding: 0px; vertical-align: baseline;"><span style="font-family: &quot;helvetica neue&quot; , &quot;arial&quot; , &quot;helvetica&quot; , sans-serif;">Yes, yes, in the quote above we were sloppy, and should have instead said “The value lies in convincing other players that you’ve been sabotaged.” It matters less who exactly caused you to be sabotaged.</span></div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">So Hanson paints me as a nitpicky philosopher, but nevertheless takes the points. He didn't mention the second point under the second heading, about theory of mind, which I think is maybe the most important. This omission better lets him get away with painting me as a nitpicky philosopher. But I am happy to see the response, and will not be daunted in making conceptual points that in fast-and-loose mode may seem like mere nitpicks.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">What may seem like mere nitpicks at the stage of airing these ideas and getting them a hearing can turn into important substantive points in the context of actually trying to develop them further and make them more robust.&nbsp;</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com1tag:blogger.com,1999:blog-8137988136860941398.post-31533744315282593642018-01-03T21:03:00.000-08:002018-01-09T15:49:00.488-08:00Two Critical Remarks on The Elephant in the Brain<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i>UPDATE: See&nbsp;<a href="http://sprachlogik.blogspot.com/2018/01/robin-hanson-responds.html">my response</a> to <a href="http://www.overcomingbias.com/2018/01/elephant-in-the-brain-reviews.html">Robin Hanson's response</a>.</i></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i><br /></i></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i><a href="http://elephantinthebrain.com/">The Elephant in the Brain</a></i>, the new book by Robin Hanson and Kevin Simler, is a fantastic synthesis of subversive social scientific insight into hidden (or less apparent) motives of human behaviour, and hidden (or less apparent) functions of institutions. Just understanding these matters is an intellectual thrill, and helpful in thinking about how the world works. Furthermore - and I didn't sufficiently appreciate this point until reading the book, despite being exposed to some of the ideas on <a href="http://www.overcomingbias.com/">Hanson's blog</a> and elsewhere - better understanding the real function of our institutions can help us improve them and prevent us from screwing them up. Lots of reform efforts, I have been convinced (especially for the case of schooling), are likely to make a hash of things due to taking orthodox views of institutions' functions too seriously.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Without trying to summarise the book here, I want to point out what I think are two conceptual shortcomings in the book. This is friendly criticism. Straightening these confusions out will, I think, help us make the most of the insights contained in this book. Also, avoiding these errors, which may cause some to be unduly hostile, in future or revised presentations of these insights may aid in their dissemination.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I'm not sure how important the first shortcoming is. It may be fairly trifling, so I'll be quick. The second one I suspect might be more important.</span><br /><b><i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></i></b><b><i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">1. Being Common Knowledge Confused With Being Out in the Open</span></i></b><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">One conceptual issue came up for me in Chapter 4, 'Cheating'. Here, around p. 55 - 57, the authors seem to conflate the concept of common knowledge with the idea of being "out in the open" or "on the record".</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A group of people have <i>common knowledge</i> of P if everyone in the group knows that P, and knows that everyone in the group knows that P, and knows that everyone in the group knows that everyone in the group knows that P, and so on.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">On the other hand, a bit of knowledge is <i>on the record</i>&nbsp;or <i>out in the open</i>&nbsp;if it is 'available for everyone to see and discuss openly' (p. 55).&nbsp;</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">The authors conflate these ideas, asserting that 'Common knowledge is information that's fully "on the record," available for everyone to see and discuss openly' (p. 55). (This comes shortly after the proper recursive explanation of 'common knowledge'.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">This seems wrong to me. Something may satisfy the conditions for being common knowledge, but people may still not be OK talking about it openly. The popular notion of an <i>open secret</i>&nbsp;gets at this point (somewhat confusingly for present purposes, since here the word 'open' gets used on the other side of the distinction). Something may be widely known, indeed even <i>commonly</i>&nbsp;known in the special recursive sense, while being taboo or otherwise unavailable for free discussion.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">In addition to muddying the proper recursive explanation by asserting that common knowledge is that which is on the record and out in the open, the authors give supplementary example-based explanations of 'common knowledge' which seem to pull this expression further towards being unhelpfully synonymous with 'out in the open' and 'on the record'. For instance when they write: 'Common knowledge is the difference between (...) a lesbian who's still in the closet (though everyone suspects her of being a lesbian), and one who's open about her sexuality; between an awkward moment that everyone tries to pretend didn't happen and one that everyone acknowledges' (p, 55). If we stick to the proper recursive explanation of 'common knowledge', these claims just seem wrong. There could be cases where a lesbian is not open about being a lesbian, yet the hierarchy of conditions for common knowledge is fulfilled. Likewise for the awkward moment that everyone wants swept under the rug.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><b><i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">2. Excessive Preconditions Posited for Adaptive 'Self-Sabotage'</span></i></b><br /><b><i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></i></b><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">The authors give fascinating, instructive explanations of how what they call 'self-sabotage' can be adaptive in some situations (pp. 66 - 67). One example they give is visibly removing and throwing out your steering wheel in a game of chicken (provided you do it first, this is a good strategy, since your opponent then knows that their only hope of avoiding collision is to turn away themselves, losing the game of chicken). Another is <i>closing or degrading a line of communication</i>, e.g. turning your phone off when you think you might be asked a favour you don't want to grant. Another is avoiding seeing your kidnapper's face so that they don't kill you in order to prevent you identifying them to authorities. Another example is a general believing, despite contrary evidence, that they are in a good position to win a battle - while epistemically bad, this may cause the general (and in turn the troops) to be more confident and intimidating, and could even change the outcome in the general's favour.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But some of the things they then say about this sort of thing seem confused or wrong to me. The underlying problem, I think, is hasty generalisation. For instance:</span><br /><blockquote class="tr_bq"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Classical decision theory has it right: there's no value in sabotaging yourself per se. The value lies in <i>convincing other players</i>&nbsp;that you've sabotaged yourself. (p. 67).</span></blockquote><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">This fits the game of chicken example pretty well.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But it doesn't really fit the turning-your-phone-off example: what matters there is that your phone is off - it doesn't matter if the person wanting the favour thinks that your phone malfunctioned and turned itself off, rather than you turning it off. Indeed having them think the former thing may be even better. But still, it might be right in this case that it's important that the person calling believes that you were uncontactable. If you have your phone off but they somehow nevertheless believe they succeeded in speaking to you and asking the favour, you may not have gained anything by turning it off.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">It similarly doesn't fit the example of the kidnapper. It doesn't really matter how the kidnapper thinks it came about that you failed to see them - they don't need to believe you brought the failure on yourself for the strategy to be good. But still, it seems right in this case that it's important that they believe you didn't see their face.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Now it <i>really</i>&nbsp;doesn't fit the example of the general, and here the failure of fit is worse than in the previous two cases. If the point is that the epistemically dodgy belief of the general makes them more confident and intimidating, potentially causing them to win, then it doesn't matter how the general got the belief. The "sabotage" could just as well be due to an elaborate ruse carried out by a small cadre of the general's subordinates. And here there's not even a 'but still' of the sort in the two previous cases. The general's epistemically dodgy belief does <i>not </i>have to be known to be epistemically dodgy by the enemy in order for it to intimidate them and cause them to lose. Indeed, that would <i>undermine</i>&nbsp;the effectiveness of the strategy!</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">So, things are not as simple as the above quote suggests. Realising this and appreciating the nuances here could pay dividends.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Another claim made about this sort of thing which may at first seem striking and insightful, but which I think does not hold up, is this:</span><br /><blockquote class="tr_bq"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Sabotaging yourself works only when you're playing against an opponent with a theory-of-mind (p. 68).</span></blockquote><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(Theory-of-mind is the ability to attribute mental states to oneself and others.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">This doesn't really fit the game of chicken example, or at least it doesn't fit possible cases with a similar structure. It may be that to truly have a game of chicken, you need theory-of-mind on both sides, but you could have a situation where you're up against a robotic car with no theory-of-mind, and it may still be best to throw out your steering wheel. (As to why you wouldn't just forfeit the "game of chicken": there may be (theory-of-mind-less) systems monitoring you which will bring about your death if you swerve.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I don't think it really fits the kidnapper case in a deep way. It may be a contingent fact that this sort of thing only works in our world with kidnappers with theory-of-mind, but one can easily imagine theory-of-mind-less animals who have <i>evolved</i>, rather than worked out by thinking, the behaviour of killing captives when seen by them.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I think it quite clearly doesn't fit the general example. Imagine the general and their army were fighting beasts with no theory-of-mind. All that matters is that the beasts can be intimidated by the confident behaviour caused by the general's dodgy belief. No theory-of-mind in the opponent required.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">This seems like more than a quibble, for going along with this mistaken overgeneralization may stop us from seeing this kind of mechanism at work in lots of situations where there is no theory-of-mind at work on the other end of the adaptive sabotage.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-43870389106427129042017-12-11T15:23:00.000-08:002017-12-11T15:23:49.047-08:00Contingent Examples of Term-Relative Intrinsicality?<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><a href="https://philpapers.org/rec/ZYLENA">Zylstra's</a> <a href="http://vermont.academia.edu/JustinZylstra">work</a> shows that, if we are going to try to analyze essence in terms of necessity and intrinsicality and deliver the goods on <a href="https://philpapers.org/rec/FINEAM-2">Fine's</a> celebrated Socrates/{Socrates} example (Socrates does not belong essentially to {Socrates}, but {Socrates} essentially contains Socrates), we had better understand intrinsicality as term-relative, at least in the case of relations. That is, we can't just say that some relations are intrinsic and others are extrinsic and that's it - rather, some two-place relations are, so to speak, intrinsic on one side but extrinsic on the other.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But can we really explicate such a concept of intrinsicality? Or is this really just going to be the concept of essence which we end up explicating? If we can do the job, then we should get something that, when supplemented with necessity, yields the notion of essence. This suggests that we should be able to find <i>contingent</i>&nbsp;cases of such asymmetric intrinsicality. And so that now seems to be the big question, if we're wondering whether essence should be accounted for in terms of necessity and something else, or the other way around. (Or at least whether intrinsicality should be involved if we pursue the first strategy.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Thinking about parts of things, where those things could nevertheless have had different parts, may be one way of looking. For instance, perhaps 'My laptop contains the chip C' provides such an example. If the chip is intrinsic to the laptop, then we can say that the laptop intrinsically contains the chip, but that the chip is not intrinsically inside the laptop. But the laptop could have had another chip or perhaps no chip in that place, so it does not contain the chip necessarily.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I wonder how solid and convincing this sort of example is, though, and I wonder if there are other sorts available.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-117471640597656282017-12-09T21:03:00.002-08:002017-12-11T15:25:02.173-08:00Sticking Up for 'Essence = Necessity + Intrinsicality' in the Face of Zylstra's Argument<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i>Followup: </i><a href="http://sprachlogik.blogspot.com/2017/12/contingent-examples-of-term-relative.html">Contingent Examples of Term-Relative Intrinsicality?</a></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i><br /></i></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i>UPDATE 11/12/2017: The more I think about Zylstra's argument, the more I think I've been overly critical, and not sufficiently open to changing my views. I have moderated some of the worst excesses by editing the below a little bit. I continue to think about the lessons which we should draw from Zylstra's argument, and may come back to the matter in a future post. One thing which has just begun to bother me is that, if we try to take the lesson to show that we'd better make intrinsicality term-relative when it comes to relations, is that the stuff which comes to mind when trying to explicate the resulting notion of "intrinsicality" - I found myself thinking things like 'x bears R to y intrinsically if part of what it is to be x is to be R-related to y' - just ends up sounding like a characterisation of essence; the necessity-ish bit seems to come of its own accord. So maybe there </i>are<i> grounds here for serious doubt about the overall E = N&nbsp;+ I approach to essence.</i></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">An interesting new paper by Justin Zylstra attempts to cast doubt on the project of analyzing essence in terms of necessity plus something else. As Fine famously pointed out, it is plausible that the set {Soctrates} essentially contains Socrates but that Socrates does not essentially belong to {Socrates}. Being a member of that set does not have enough to do with Socrates as he is in himself, we might say, to count as an essential property of Socrates. Nevertheless, Socrates necessarily belongs to {Socrates}; in no possible world do we find Socrates but not the set containing him.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">So essential properties aren't just the necessarily-possessed properties, or so it seems. Fine makes the further proposal that we give up trying to analyze essence in terms of necessity and instead go the other way around. But others have accepted that the essential properties aren't just the necessarily-possessed ones, but sought to supplement the analysis of essence in terms of necessity. I am sympathetic to this approach, and particularly to the idea - prominently defended by Denby - that essence = necessity&nbsp;+ intrinsicality. Let's call this <i>the E = N&nbsp;+ I approach</i>.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(Denby, it is important to note, favours an account of intrinsicality on which the property of containing Soctrates is <i>not</i>&nbsp;intrinsic, but <i>ex</i>trinsic, to {Socrates}. This leads him to push back against the <i>prima facie</i>&nbsp;plausible Finean thesis that containing Socrates is essential to {Socrates}. In my view, this was a mistake on Denby's part, and we should instead try to understand 'intrinsic' in such a way that it <i>does</i>&nbsp;come out true that the property of containing Socrates is intrinsic to {Socrates}.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">You can imagine my interest in Zylstra's paper, which is supposed to cast serious doubt on this approach. Here I want to explain why I think it does no such thing. I won't reconstruct Zylstra's detailed and technically sophisticated argument in full. To fully assess what I'm saying, in particular to verify that I speak the truth about what Zylstra does in his paper, you'd have to look at the paper.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">To understand why Zylstra's argument goes as wrong as I think it does, it helps to note that he aims his criticisms more generally at <i>any</i>&nbsp;attempt to supplement a necessity-based analysis of essence so that it delivers the goods on Fine's celebrated examples, provided it is of a certain general form. He intends this form to cover the E = N&nbsp;+ I approach. The trouble is, it is very easy to formulate a version of that approach which does not take general form in question.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">The central problem with Zylstra's handling of the E = N + I approach is that he considers only Denby's version, which proceeds as if the relevant notion of intrinsicality can be treated as a sentential operator. It is intrinsic that <i>p</i>. But no friend of the E = N&nbsp;+ I approach should want to do that.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">The whole point of bringing in intrinsicality, I would have thought, is that it is plausibly intrinsic to {Socrates} that it contains Socrates, but not intrinsic to Socrates that he is contained by {Socrates}. But if we represent our idea of intrinsicality as a sentential operator, all we can say is:</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">It is intrinsic that Socrates is a member of {Socrates}.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">or</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">It is intrinsic that {Socrates} contains Socrates.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">or whatever.<br /><br />Now, this doesn't really even make sense without explanation, but putting that aside, and assuming that such claims will either be true or be false, Zylstra is able to show that an analysis of essence in terms of necessity and this weird intrinsicality sentential operator can't deliver the goods.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But so what? This just shows that the relevant notion of intrinsicality can't be captured as a sentential operator! Indeed, in his last section, entitled 'A glimmer of hope', Zylstra suggests that instead of supplementing a necessity-based analysis of essence with a notion that can be expressed as a sentential operator, we <i>might</i>&nbsp;be able to use an operator that takes a sentence and a noun phrase and produces a sentence:</span><br /><blockquote class="tr_bq"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Recall that the <i>Supplemented Necessity Analysis</i> involved an existentially bound variable <i>O</i> that functions syntactically as a monadic sentential operator. But nothing prohibits us from introducing a further type of variable <i>Xt</i> that functions syntactically as a binary term-sentence operator. (Zylstra (forthcoming), Section 5.)</span></blockquote><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Considering as he is all analyses of the relevant, sentential-operator form, rather than just the weird instrinsicality-as-a-sentential-operator instance, he never comes back to consider that maybe the E = N + I approach should be pursued with a binary term-sentence operator. (Another reason for Zylstra's neglecting to do this, perhaps, is that it is Denby's version of the approach that Zylstra considers, and that version - ill-advisedly, as I suggested in a parenthesis near the beginning of this post - fails to deliver the intuitive Finean verdict that containing Socrates is essential to {Socrates}.) But really, that's just the natural view when you think about this. The weird sentential-operator form is just an especially bad version of the E = N + I approach which no one sympathetic to that approach should allow.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I conclude that Zylstra's new paper poses no real threat at all to the E&nbsp;= N&nbsp;+ I approach to understanding essence.&nbsp;</span><span style="font-family: &quot;georgia&quot;; vertical-align: baseline; white-space: pre-wrap;">Rather, the lesson that the friend of the E = N + I approach should draw is that intrinsicality is not to be expressed using a monadic sentential operator. Nor will it do to think of it, in general, as something which relations possess or fail to possess </span><span style="font-family: &quot;georgia&quot;; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">tout court</span><span style="font-family: &quot;georgia&quot;; vertical-align: baseline; white-space: pre-wrap;">. A relation like the set-membership relation is, so to speak, extrinsic on Socrates’s end but intrinsic on {Socrates}’s end. </span><br /><span style="font-family: &quot;georgia&quot;; vertical-align: baseline; white-space: pre-wrap;"><br /></span><span style="font-family: &quot;georgia&quot;; vertical-align: baseline; white-space: pre-wrap;">In a way, this is really just a criticism about emphasis. Rather than presenting his argument as if it were a serious threat to the E = N + I approach, and then offering a 'glimmer of hope', Zylstra should, in my view, have just presented his argument as showing something instructive about how a friend of the E = N + I should, and should <i>not</i>, try to formulate it.</span><br /><div><span style="font-family: &quot;georgia&quot;; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><b>References&nbsp;</b></span></i><br /><i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: white; color: #333333;">Denby, David A. (2014). Essence and Intrinsicality. In Robert Francescotti (ed.),&nbsp;</span><em style="background-color: white; box-sizing: border-box; color: #333333;">Companion to Intrinsic Properties</em><span style="background-color: white; color: #333333;">. De Gruyter. pp. 87-109.</span>Author-archived version currently available open-access at&nbsp;<a href="http://philpapers.org/rec/DENIAE-3">http://philpapers.org/rec/DENIAE-3</a>.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: white; color: #333333;">Fine, Kit (1994). Essence and modality.&nbsp;</span><em class="pubName" style="background-color: white; box-sizing: border-box; color: #333333;">Philosophical Perspectives</em><span style="background-color: white; color: #333333;">&nbsp;8:1-16.</span></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: white; color: #333333;">Zylstra, Justin (forthcoming). Essence, necessity, and definition.&nbsp;</span><em class="pubName" style="background-color: white; box-sizing: border-box; color: #333333;">Philosophical Studies</em><span style="background-color: white; color: #333333;">:1-12. Currently available open-access at the author's Academia.edu page, the URL of which is currently&nbsp;</span><span style="color: #333333;"><a href="http://vermont.academia.edu/JustinZylstra">http://vermont.academia.edu/JustinZylstra</a></span><span style="background-color: white; color: #333333;">.</span></span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-4482321990563504572017-11-09T06:21:00.000-08:002017-11-10T05:33:26.572-08:00Two-Dimensional Semantics and Counterfactual Invariance Deciders<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">For a long time I have wondered, with an uneasy feeling that there was something I couldn't see, about the relationship between two-dimensional semantics and my approach to analysing subjunctive necessity <i>de dicto</i>. As I flagged in the <a href="http://sprachlogik.blogspot.com/2017/11/old-account-may-not-be-false-after-all.html">previous post</a>, this has become even more urgent in light of my <a href="http://sprachlogik.blogspot.com/2017/09/a-new-account-of-conditions-under-which.html">new, relational account</a> involving the notion of a counterfactual invariance (CI) decider.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I think I've finally made a breakthrough here, and found a clear connection. There is more to say, but here it is briefly.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Recall that my account states that a proposition is necessary (i.e. necessarily true or necessarily false) iff it has a true positive counterfactual invariance (CI) decider.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(P is a positive counterfactual invariance decider for Q iff Q does not vary across genuine counterfactual scenario descriptions for which P is held true.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A close analogue of this account can be stated in terms of <a href="http://consc.net/papers/twodim.html">two-dimensional semantics</a>: a proposition Q is necessary iff there is a true proposition P such that for every scenario S in which P is true, Q's two-dimensional intension maps, for all W, &lt;S, W&gt; to the same truth-value.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">And I think I can maintain, as CI deciderhood is plausibly <i>a priori </i>tractable and arguably a semantic matter, so too is the question whether, given some propositions P and Q, P is such that for every scenario S in which P is true, Q's two-dimensional intension maps, for all W, &lt;S, W&gt; to the same truth-value.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">This makes clear one major way in which my analysis goes beyond the normal two-dimensional account of subjunctive necessity in terms of secondary (or C) intension - and this way can then be translated into two-dimensional terms. And looking at necessity this way, as opposed to with just the usual two-dimensional account of subjunctive necessity, gives us a finer grained picture of the role played by what Kripke called '<i>a priori</i>&nbsp;philosophical analysis' in our knowledge of necessity. You don't have to know which scenario is actual to know that a proposition is necessary - you just need to know that you're in one of some range of scenarios such that, if they were actual, the proposition would be necessary. And such a range can be characterized by a proposition which you can know <i>a priori</i>&nbsp;to be a CI decider for the necessary proposition in question.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-71321384581943777342017-11-06T20:01:00.001-08:002017-11-07T16:28:48.695-08:00Old Account May Not Be False After All, But New One Still Better (and New Frontier: Relation to Two-Dimensionalism)<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Last Thursday I gave a talk at Sydney University's philosophy department about <a href="http://sprachlogik.blogspot.com/2017/08/kippers-bombshell.html">Kipper's bombshell</a>, my old account of necessity, and <a href="http://sprachlogik.blogspot.com/2017/09/a-new-account-of-conditions-under-which.html">my new account</a> involving counterfactual invariance deciders. I was asked many good questions and got a lot out of it.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">In preparing the talk, I came to realise that I may have been too quick to assume that 'Air is airy' disproves my old account, according to which a proposition is necessarily true iff it is in the deductive closure of the set of propositions which are both true and inherently counterfactually invariant. Because 'There is nothing more to being air than being airy' is plausibly true and ICI, and it does - at least on a rich enough notion of impication - imply 'Air is airy'.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Now, if that's right, what follows? Are my new ideas about abandoning, in the analysis of necessity, the property of ICI for a relation of deciderhood, to be thrown out? I don't think so. Even if I was pushed towards them by the possibly wrong idea that my old account can't be defended from 'Air is airy', they still seem to give us an account which seems better. The old account now seems clumsy, so to speak. Maybe it can be understood in a way - with a rich notion of implication - so that it doesn't go wrong on 'Air is airy'. But this still seems like a kind of lucky break, and it's not clear to me that there aren't more threatening examples in the offing. The new account, on which a proposition is necessary iff it has a true positive counterfactual invariance decider, seems to reveal the notion's workings more faithfully, and seems less hostage to as-yet-unconsidered examples.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(Also note that, with the new account, you <i>can</i>&nbsp;use 'There's nothing more to being air than being airy' as your decider, but it seems like you can also use something like 'Air has no underlying nature' or 'Air is not a natural kind', and these do <i>not</i>&nbsp;seem to imply 'Air is airy' - they do not seem to contain that information. And since it seems you can plug <i>these</i>&nbsp;into the new account and conclude that 'Air is airy' is necessary, but cannot conclude the same on the same basis with the old account, that the new account is superior here, in enabling us to conclude necessity on a sometimes slenderer basis than we can using the old account.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">In the talk I gave, there were a number of questions and examples suggested which could look like they may disprove my account, but I was able to respond to all of them straightforwardly and to my account's credit. (With some elements of the new account, it's hard to see immediately why they're there and are as they are, but working through some examples clarifies things.) I also fielded a question (thanks to N.J.J. Smith) about how my account goes beyond what we already find in Kripke. There too I was able to give what I think is a satisfactory answer: the account isolates a plausibly <i>a priori</i>&nbsp;tractable, maybe broadly semantic, aspect to necessity. Kripke's work doesn't do this. He says a proposition is necessary if it holds in all the ways things could have been, and one of his main points is that we don't in general know <i>a priori</i>&nbsp;what these ways are. True, he also allows that we know by '<i>a priori</i>&nbsp;philosophical analysis' (this occurs in 'Identity and Necessity') that 'Hesperus is Phosphorus' is necessarily true if true at all, but that isn't true of all examples. You might thus wonder, with respect to examples that <i>don't</i> work that way, what part '<i>a priori </i>philosophical analysis' might play in our knowledge of <i>their</i> modal status. My account gives us an answer to this.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But another sort of question arose in the talk was how my account relates to two-dimensional semantics, and I was less satisfied with what I had to say on that.&nbsp;</span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">The true CI deciding proposition(s) in my account seem to play a role close to the role played by what world is actual in two-dimensional semantics.&nbsp;</span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">&nbsp;I worry that some in the audience were beginning to suspect that I've just laboriously re-arrived at two-dimensionalism along a somewhat different path. (And I'm getting a bit suspicious myself.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br />So, I think that now, the most pressing task is to clarify the relationship of my new account to two-dimensional semantics, rather than to defend it further from counterexample. (This has always been a background concern, even with my old account, but now it has become urgent.) The notions in my account come up in a different way, and most formulations of two-dimensionalism seem to bring up difficulties which I may be able to avoid. My account seems more minimal and focused on its topic, and thus potentially more instructive.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Such anyway is my hunch, but it remains to make this clear.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-17081953322794234102017-09-21T21:15:00.001-07:002017-09-22T06:23:20.278-07:00A Dialogue on Mathematical Propositions<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i>I wrote the following dialogue as an antidote to the dogmatism I felt myself falling into when trying to write a paper about&nbsp;</i>a priori<i>&nbsp;propositions</i>. <i>The characters A and B are present-day analytic philosophers. Roughly, A represents the part of me which wanted to write the paper I was working on, and B represents the part which made trouble for the project.</i></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: I've got a view about <i>a priori</i>&nbsp;propositions I'd like to discuss with you. I don't think you're going to like it.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: Intriguing! I'll try to put up a good fight.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: Good. Still, you won't just defend the opposite view no matter what, will you? I'm certainly going into this ready to modify my view, if not to completely relinquish it.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: Sure. No, I won't just set myself up as an opponent debater. Let's try to give each other as much ground as our philosophical consciences allow, and see if we can agree on some things.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: OK, great. So, here's the view: what is special about <i>a priori </i>propositions, which enables them to be known independently of experience, is that they have their truth values essentially. They do not reach outside themselves to get their truth values, but carry them within as part of their nature.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: OK. Interesting use of the notion of essence. I'm used to associating views which tie <i>a priori</i>&nbsp;propositions' truth or falsity closely to meaning with more deflationary attitudes, not with philosophers who make positive use of metaphysical notions like that of essence.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br />A: Exactly. That's one of the exciting things about my view, I think. It brings out the fact that that sort of tight connection between meaning and truth value can be posited without embracing any problematic conventionalist or deflationary attitudes about essence or meaning.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: I think you have a point there. A meaning-based view of <i>a priori</i>&nbsp;truth doesn't need to be deflationary or conventionalist. Still, I think it's wrong. Your view overlooks the fact that <i>a priori</i>&nbsp;propositions, or many of them at least, are about something, and we often have to inquire into that something to know them. When mathematicians discover new truths, they don't sit and try to get insight into the essences of the propositions they are wondering about. They try to get insight into the things that the propositions are about, like numbers, or sets, or graphs.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: That is true, but does not affect what I am saying. Look, the&nbsp;<i>a priori </i>truths of mathematics either have their truth essentially, or accidentally. And if they really had to reach outside themselves for their truth, then they would only be true accidentally. And in that case it should be possible to depict those very propositions reaching out but getting the opposite truth value. But you can't even begin to imagine a situation where someone has expressed what is actually an <i>a priori </i>truth, but which in that situation is a false proposition. And it's not like the case of propositions whose instantiation vouchsafes their truth, like 'Language exists'. Instead, their truth is of their very essence. Now, we all agree that an <i>a priori</i>&nbsp;truth can have its actual truth value, but what would it look like for it to have the other one? The onus is on you to flesh out an answer here, and it seems to me that nothing you could say on this point would satisfy.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: I do not dispute that I couldn't really flesh out a description of a situation where the same <i>a priori</i>&nbsp;proposition gets the opposite truth value, but I don't think I have to be able to.&nbsp;I can still maintain that these <i>a priori</i>&nbsp;truths do not have their truth off their own bat, due to meaning alone. The source of their truth lies in what they are about. <i>However</i>, unlike with empirical truths, what they are about is rigid and unmoving - necessarily the way it is. So it is no real objection that I cannot depict a situation in which their source of truth or falsity yields them a different truth value, since that is just because their source is necessarily the way it is. That doesn't make their source any less of a source.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: So you are saying that the meanings of these <i>a priori </i>propositions are out there in a rigid, unmoving space of possible meanings, and that they get their truth or falsity from an equally rigid, unmoving space of mathematical objects. But since all this stuff is rigid, unmoving, and necessarily the way it is, it seems to me that your talk of sourcing is just empty talk. The very idea of sourcing seems dubious here. Granted, you may <i>seem</i> to have an advantage in the fact that our <i>knowledge</i>&nbsp;of these truths must have some source. But the sourcing you are talking about is all going on in Plato's Heaven. It does nothing to explain how we get the knowledge. So you might as well not posit it.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: You are trying to cast aspersions on my talk of sourcing, but I want to suggest that what you are saying is, on examination, more dubious than what I am saying. You are no nominalist, no denier of the independent existence of mathematical objects. Right?</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: Sure. I mean, I think when people object to claims like 'Mathematical objects exist independently', they are perhaps bothered by something that really should bother them. But I do think that understood properly, such claims do make a sound and correct point.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: OK, fine. And so, it seems to me that if you are saying that <i>a priori</i>&nbsp;truths about these objects have their truth essentially and off their own bat, you are positing a kind of <i>harmony</i> between the meanings and what they carry inside them on the one hand, and the mathematical objects on the other. But this harmony seems dubious. It cries out for explanation. Why should it exist? Coming around to the proper view, that the propositions are about the mathematical objects, and therefore the mathematical objects' being the way they are is the source of these propositions' truth values, the difficulty disappears.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: I don't see how the harmony you complain about is particularly strange or objectionable. Don't parts of mathematics mirror and reflect each other in weird and wonderful ways? Since we accept that, it seems that it's not particularly costly to acknowledge that the meanings of mathematical truths are also part of this crystalline structure. Crucially, it seems less dubious than your sourcing talk - more of a piece with things we already acknowledge. And it seems to me that your view overdoes the analogy between mathematical and empirical truths, leading to confusion.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: Do you see any positive value in your view? Or is it all about stopping that over-assimilation?</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: Well, perhaps my view helps with the problem of how we get mathematical knowledge. It seems to me an easier problem to say how we get in touch with meanings, than to say how we get in touch with things like numbers and sets. Our talk and thought <i>instantiates</i>&nbsp;meanings, I want to say, even if the meanings themselves are abstract, like numbers and sets.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: But there are also "instantiation relationships", arguably more straightforward, between, say, numbers and piles of apples.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: Hmm. Well, I don't know, I'll have to think more about that - but perhaps stopping the over-assimilation is enough. What value do you see in your view, anyway?</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: When I think about what is fundamentally wrong with your view, apart from my complaints about it being mysterious and ill-motivated, it seems to me that, in your effort to block the over-assimilation of mathematical and empirical propositions, you bring about <i>another</i> over-assimilation. Namely, between mathematical propositions which can be hard to discover the truth about, and what you might call paradigmatically analytic propositions - propositions where it really does seem that the way to know the truth about them is just to have insight into their meanings. <i>Those</i>&nbsp;propositions may perhaps be said to have their truth values essentially, since they don't seem to say anything substantial about anything, whether their subject matter be empirical or mathematical. And your view wrongly depicts substantial mathematical propositions as being like them. My view has the virtue of avoiding that over-assimilation. It may be that the over-assimilation you worry about is also a problem, but it should be combated in a different way.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: Well, I am - or at least have been, up to having this conversation - inclined to think the corresponding thing about the over-assimilation that <i>you</i> are worried about. Positing a mysterious sourcing relationship between mathematical propositions and mathematical objects seems like a crude expedient. But I must acknowledge that the over-assimilation that bothers you is also a problem.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: OK. So, it seems we can both agree that our respective views may have some power to prevent a certain over-assimilation, a different one in each case. And perhaps we can also agree that each of our respective views, when adopted, may increase the danger of falling into the over-assimilation targeted by the opposite view.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: Hmm. I suppose we can both agree about that.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: Now, isn't this worrying? I mean, where does it leave us? We have a question: Do mathematical propositions have their truth values essentially, intrinsically, inherently, off their own bat - or do they not? And it seems like our opposing answers have opposing strengths and opposing weaknesses. I feel the weakness of your view much more acutely, but I can't deny that your feeling that my view might be a somewhat crude expedient makes some sense as well.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: I'm glad you're staying true to your intention of not just defending your view tooth and nail. Now it's starting to look like both our views have some merit, but that these merits crowd each other out. I am beginning to think that perhaps both our views can be said to suffer from crudeness on that score. We are both inclined to use a certain picture to ward off the over-assimilation which has most bothered us. And the pictures conflict, or at least seem to. Now, could it be that if our views were made clearer, these pictures could be seen to apply in different ways, so that there is no inconsistency in using one in its way, and the other in <i>its</i>&nbsp;way? The task then would be to clarify the difference between these two ways of using what appear to be conflicting pictures.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: That is sounding more and more reasonable to me as a diagnosis of what's going on in this case. How <a href="https://en.wikipedia.org/wiki/Ludwig_Wittgenstein">Wittgensteinian</a>! And to be honest, the Wittgensteinian-ness of this view worries me a bit, since this sort of approach, to this sort of problem, seems like it will turn many people off right away. If we are to try to resolve our difficulties this way, and if we expect the resolution to be given a fair hearing, I suppose we will also have to be careful to defend our resolution from objections which lump it together with features of Wittgenstein's views which people don't like.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: I agree that is a worry. And it may be even worse than you are suggesting. What if the things people don't like and have turned their back on include this very power to resolve our difficulties!</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: Well, I see what you're saying. People are invested in a certain way of doing things, and in defending views of a certain type. And those ways of doing things may come naturally, at least to people with a certain background (including us), so that one slides back into them. But I think we may just have to try to give the naysayers about this method plenty of credit, and allow that there are serious problems with the sort of resolution we're talking about now. After all, why wouldn't there be? It could be that it's very promising, and still ultimately our best hope, but that there are serious difficulties with it which, in our desire to resolve our present issue, we aren't currently alive to.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: I suppose I'm on board with what you're saying. As exciting and powerful as this approach may seem now, we must beware of coming off as if we think there's a silver bullet, a simple solution we've already got here. And I think that comes out more clearly when we come back from talking about pictures and consider the question, framed in terms of 'essence' or 'intrinsic' or what have you. Something about the idea of pictures makes us quite willing to allow different applications. Ambiguities, if you like. But it seems as though people, ourselves included, may be inclined to take a certain attitude to words like 'essence' and 'intrinsic', such that the word analogue of the move where we say 'These pictures appear to conflict, but if you look at their application, you see it's only an apparent conflict' seems less appealing. There is a feeling that with such words that for each there is a big, important, single job that they should be doing.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: I think you're right. But again, I think you may be overplaying people's resistance. Yes, there will be people who just get turned off at the suggestion that such words should be understood as having various quite important roles to play. But probably, with many of the sort of people you have in mind, you must admit that they <i>are </i>willing to countenance such things as long as you keep things relatively clear and definite. I mean, if you start banging on about how complex and multifaceted it all is with these words, then yes, that will turn people off, because it sounds defeatist. It sounds like shirking hard and maybe very interesting work. But these sorts of people - and let's face it we're among them a lot of the time when we aren't just talking but trying to write papers - are quite willing to distinguish certain senses of weighty-seeming words, using little subscripts for example. So we shouldn't be too discouraged.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: Yes, I suppose that's right. So, we should be ready to float the idea that our different pictures each having a role to play, but that just giving the picture and saying 'That's how things are' is a bit crude until we clarify and distinguish the application of the picture in each case. And we should be ready to try to take exactly this approach when it comes to our difficulties as posed in philosophical jargon, but be on guard against defeatist or wishy-washy sounding attitudes. I confess I'm worried about the extent to which this is possible. I mean, maybe once we try, we will find that the distinctions we might want to make by putting little subscripts on words like 'essence' tend to fall apart in our hands, or that possibilities multiply very quickly. But on the other hand, I must admit we haven't seriously tried yet. And maybe there is some progress to be made in that way, even if it does give out and get confusing again in a way similar to our original disagreement. So we should keep working on this.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: Agreed.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: I think I'm pretty worn out for now, though. And I suspect there are further problems with your view that I haven't brought out.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: Same here, on both counts.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A: I hope we can find what it takes to continue soon.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">B: So do I.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com5tag:blogger.com,1999:blog-8137988136860941398.post-23280450358134342172017-09-11T21:02:00.000-07:002017-10-25T21:29:06.576-07:00A New Account of the Conditions Under Which a Proposition is Necessary<i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">The previous posts were quite raw and had me wrestling with new data. In this post, I try to be clearer and more accessible, and give a first outline of a new account of necessity that has emerged from my research on these topics.&nbsp;</span></i><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">My old account of necessity was:</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A proposition is necessarily true iff it is, or is implied by, a proposition which is both inherently counterfactually invariant (ICI) and true.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A proposition P is ICI iff &nbsp;P's negation does not appear in any (genuine) counterfactual scenario description for which P is held true.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(I.e. if you hold P true, then you won't produce (genuine) CSDs in that capacity (of holding P to be true) according to which not-P.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(You might wonder about what exactly a CSD is and what it takes for one to be genuine, but this will not be our focus here.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">This account nicely handles an example like 'Hesperus is Phosphorus or my hat is on the table'. This proposition isn't itself ICI - after all, you can hold it true by holding it true that my hat is on the table but Hesperus is not Phosphorus, and in that case you'd be prepared to produce CSDs in which it's false. But it <i>is</i>&nbsp;implied by a true ICI proposition, namely 'Hesperus is Phosphorus'.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">The account also handles more complicated cases where there is no <i>component </i>ICI proposition (as there happens to be in the last example). It is enough that a true ICI proposition <i>implies </i>the necessary truth we are interested in.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But this account recently fell, due initially to an example from Jens Kipper (discussed in <a href="http://sprachlogik.blogspot.com/2017/08/kippers-bombshell.html">recent</a> <a href="http://sprachlogik.blogspot.com/2017/09/strohminger-yli-vakkuri-improve-upon.html">posts</a> <a href="http://sprachlogik.blogspot.com/2017/09/the-importance-of-counterfactual.html">here</a>). The example is 'Air is airy'. The point of this sentence is that it denotes something which isn't a natural kind - i.e. has no particular underlying nature - and predicates of it its superficial properties. Since, as it turns out, air isn't a natural kind, 'Air is airy' is necessarily true; there couldn't have been non-airy air, since, as it turns out, what is is to be air is just to be airy. If on the other hand air had turned out to have an underlying nature, like water does, we would regard 'Air is airy' as contingent, like we do 'Water is watery'; there could have been non-watery water, i.e. H20 in a situation where it isn't watery.&nbsp;</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">The problem for my old account is that 'Air is airy' is necessarily true, but it is neither ICI nor is it implied by an ICI true proposition.&nbsp;</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(After the Kipper example, I have also come upon an example due to Strohminger and Yli-Vakkuri: 'Dylan is at least as tall as Zimmerman'. Since Dylan is Zimmerman, this is necessary. But it isn't ICI, since you could hold it true while holding that Dylan and Zimmerman are distinct. With this example, you could try to save my account by maintaining that - in a rich sense of 'implies' - this troublesome example is implied by 'Dylan is Zimmerman' (which is true and ICI), so my account gives the right answer after all, provided we have the rich sense of 'implies' on board. But I see little point in this, as this trick doesn't help with 'Air is airy'.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">What I think all this shows is that, in our analysis of necessity, we need, not the notion of implication, but more specialised relevant relationships between propositions. In particular, we need to consider when the truth of a proposition P would make a proposition Q necessary. Or, for a more penetrating analysis, when P would make Q counterfactually invariant.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Let's say that P is a <i>positive counterfactual invariance decider </i>for Q iff Q does not vary across genuine CSDs for which P is held true.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(A proposition P&nbsp;<i>varies</i>&nbsp;across a bunch of CSDs iff it is true according to some of them but not according to others.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br />So, for example, 'Hesperus is Phosphorus' is its own positive CI decider; if you hold it true, then, in that capacity of holding it true, you won't produce any genuine CSDs according to which Hesperus is <i>not</i>&nbsp;Phosphorus. ('Hesperus is not Phosphorus' is also a positive CI decider for 'Hesperus is Phosphorus', although it happens to not be true.) But really, these are vacuous cases; since 'Hesperus is Phosphorus' and 'Hesperus is not Phosphorus' are <i>inherently</i>&nbsp;counterfactually invariant, <i>any</i>&nbsp;proposition you like counts (on the above definitions, which may not be optimal) as a positive CI decider for these.</span><br /><span style="font-family: georgia, &quot;times new roman&quot;, serif;"><br /></span><span style="font-family: georgia, &quot;times new roman&quot;, serif;">(</span><span style="font-family: georgia, &quot;times new roman&quot;, serif;">UPDATE 26/10/2017: This last claim is false. Some random proposition like 'Snow is white' actually doesn't count as a positive CI decider for 'Hesperus is Phosphorus', since you might hold it true but not hold 'Hesperus is Phosphorus' true. If CI deciderhood had been defined by referring to the genuine CSDs in which P (the potential decider)&nbsp;</span><i style="font-family: georgia, &quot;times new roman&quot;, serif;">and</i><span style="font-family: georgia, &quot;times new roman&quot;, serif;">&nbsp;Q (the potentially decided) are held true, rather than just P. )</span><br /><span style="font-family: georgia, &quot;times new roman&quot;, serif;"><br /></span><span style="font-family: georgia, &quot;times new roman&quot;, serif;">The notion comes into its own with non-ICI propositions:</span><br /><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">'Hesperus is Phosphorus' a positive CI decider for 'Hesperus is Phosphorus or my hat is on the table'; if you hold the former true, you won't let the latter vary across CSDs.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">'Hesperus is not Phosphorus' is a negative CI decider for 'Hesperus is Phosphorus or my hat is on the table'; if you hold the former true, you will let the latter vary across CSDs (depending on whether my hat is on the table or not in the scenarios being described).</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">'Hesperus is Phosphorus' is a negative CI decider for 'Hesperus is not Phosphorus or my hat is on the table', and 'Hesperus is not Phosphorus' is a positive CI decider for 'Hesperus is not Phosphorus or my hat is on the table'.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Furthermore, this apparatus gives us good things to say about Kipper's counterexample to my old account:</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">'Air is not a natural kind' is a positive CI decider for 'Air is airy'; if you hold the former true, then the latter won't vary across CSDs.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(UPDATE 26/10/17: This last claim may be faulty, because you could perhaps hold 'Air is not a natural kind' true and also hold 'Air is not airy' true. This depends on how 'airy' is defined - is it part of its meaning that to be airy is to have the actual properties that <i>air </i>has, whatever those are? Then maybe you couldn't really coherently hold it false. But if it's defined in terms of a list of properties that we think air has, then you could get all skeptical the way Kripke does with cats and hold it true that air actually doesn't have these properties and it's some elaborate ruse which makes us think it does. This could be gotten around by narrowing our attention in the definition of positive CI deciderhood to genuine CSDs where, not just P (the potential decider) is held true, but also Q (the potentially decided). However, I don't think that this is required to save the analysis as formulated in this post, since we can just give up on 'Air is not a natural kind' itself being a CI decider (at least all by itself) of 'Air is airy' and instead appeal to 'All there is to being air is to be airy' or even just 'Air is airy and is not a natural kind'.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(Likewise for the Strohminger/Yli-Vakkuri example: 'Dylan is Zimmerman' is a positive CI decider for 'Dylan is at least as tall as Zimmerman'.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I think a good account of necessity can now be given as follows:</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A proposition is necessary (i.e. necessarily true or necessarily false) iff it has a true positive CI decider.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Note: it seems plausible that CI deciderhood is an <i>a priori</i>&nbsp;tractable matter; whether some P is a CI decider for some Q, and if so whether it is a positive or a negative decider, seem to be the sort of thing we can work out <i>a priori</i>. What we might not be able to know <i>a priori</i>&nbsp;is the truth-values of P and Q.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I will keep working on the best way to present this sort of approach, but I think the essentials are now in place.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-87265803957708281362017-09-06T00:15:00.000-07:002017-09-06T05:49:57.288-07:00The Importance of Counterfactual-Invariance Deciders<span style="font-size: small;"><i>This post contains my efforts to fix my account of subjunctive necessity </i>de dicto<i> in the wake of troublesome examples from Kipper, Strohminger, and Yli-Vakkuri. Further work is needed before I can give a good, freestanding presentation of the new account that seems to be emerging. Still, I have hopes that here I have finally found an approach capable of yielding a true analysis of this notion. Note that the talk of the 'link' refers to <a href="http://sprachlogik.blogspot.com/2017/08/an-adventure-in-linking-necessity-to.html">this</a> less ambitious project which shares some features with my project of giving an analysis of subjunctive necessity </i>de dicto<i>.</i></span><br /><span style="font-size: small;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: small;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">The <a href="http://sprachlogik.blogspot.com/2017/09/strohminger-yli-vakkuri-improve-upon.html">Strohminger/Yli-Vakkuri example</a> seems more straightforward as a counterexample when it comes to <a href="http://sprachlogik.blogspot.com/2017/08/an-adventure-in-linking-necessity-to.html">Casullo’s proposal</a>, but maybe less so than <a href="http://sprachlogik.blogspot.com/2017/08/kippers-bombshell.html">Kipper’s original ‘Air is airy’</a> when it comes to my link and (more importantly) my account, which appeal to implication.</span></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: small;"><br /></span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: small;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">The reason for that is that you can argue that there is a good sense of ‘implication’ on which:</span></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">‘Bob Dylan is Robert Zimmerman’</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">implies</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">‘Bob Dylan is at least as tall as Robert Zimmerman’</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">And then, if you wanted to defend my link or my account from this sort of counterexample alone, it would be enough to make a good case that there is such an implication relation, and do an adequate job of characterising this relation or conveying the idea of it.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">And the idea is that this implication relation would be just as must-ish, just as free from non-</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">a priori</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> elements, as a more austere formal notion of implication where only subject-neutral terms are allowed to play a role in making the implication hold.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But, would that move work to defend my link and account from the Kipper example ‘Air is airy?’. If not, we shouldn’t bother, and should instead look for a fix which handles both sorts of examples as neatly as possible.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">Another desideratum for a fix would be to retain an isolable </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">a priori</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> element, or elements (as ICI and implication are supposed to be in my original account).</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">OK, so that is a reasonable basis on which to proceed. We know roughly what we want and have a couple of ideas for how to perhaps modify the link and account. Now, to consider whether a parallel move - parallel to claiming that ‘Dylan is Zimmerman’ implies, in the relevant sense, ‘Dylan at least as tall as Zimmerman’ - could be made with ‘Air is airy’.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">So what would the argued implier be?</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">‘Air is not a natural kind’?</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">‘Air is heterogenous’?</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">‘Air has no particular underlying nature’?</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">These suggestions all provide the missing piece of information, which you would need to conclude that ‘Air is airy’ is necessary. But it seems weird to say that they imply ‘Air is airy’ in any natural sense. On the way of thinking behind Kipper’s example (which I propose to just work with as much as possible, since I want a way of defending my account or a successor to it which does not rely on rejecting that way of thinking), ‘Air is airy’ is </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">a priori</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> in any case, and is a sort of allusion to an unpacking of ‘air’ (in 2D terms, its A-intension). All the extra information, that air isn’t a natural kind or isn’t homogenous or whatever, gives us is that this thing, which we could already know to be </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">a priori</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">, is necessary, since we aren’t fixing on some underlying nature in our use of ‘air’ in counterfactual scenario descriptions.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Now, there is a feeling that, when you don’t know whether air is a natural kind or not, you’re as it were in a superposition between two notions, not quite having either. Following this idea, you might wonder whether ‘Air is airy’ might not be ICI after all, in the way we understand it once we know that air isn’t a natural kind. It’s just that, before we knew that, we used ‘Air’ with an incomplete or a not-completely-determinate meaning, such that on one filling in - that which we would get if air turned out to be a natural kind after all - ‘Air is airy’ comes out contingent, and on the other - the (presumably) actual one - the same sentence comes out necessary.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I am inclined to think that there is some sort of internally consistent position to be had that way, but the worry is perhaps that then the position ends up being about things which aren’t normally the things we are most interested in, or that it ends up employing unusual concepts, e.g. an unusual conception of ‘proposition’ which individuates them in a way finer than comes naturally (e.g. so that ‘Air is airy’ is a different proposition depending on whether we believe air is a natural kind or not). And then we might also get weird results, such as that ‘Air is a natural kind’ is <i>a priori</i> (as we mean it once we know it!).</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">So, what I am more interested in is sticking with a way of thinking which allows that we already have the proposition ‘Air is airy’ on board, fully-fledged, before we know whether air is a natural kind, and that discovering that it isn’t gives us a partly </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">a posteriori</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> basis for our knowledge that it’s necessary. I want an account of necessity which allows for this, if possible.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">Still, and especially when combined with my doctrine of <a href="http://sprachlogik.blogspot.com/2014/03/kripkes-puzzle-and-semantic-granularity.html">flexible granularity</a>, it is nice to know that - as a last resort - I can defend my account more or less as it stands by insisting on “rich” implication (to handle the Dylan/Zimmerman example) and by holding that the account works with the Kipper stuff </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">provided</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> a granularity fine enough to distinguish ‘Air’ before and after the discovery. Likewise, Strohminger &amp; Yli-Vakkuri have problems with the Kipper case, problems which I could try to go along with. But none of this is satisfying.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">One key fact which seems highly relevant is this: while it seems false that, however you hold ‘Air is airy’ true, you will hold it fixed across CSDs, it seems true that </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">if</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> you hold it true by, or as well as, holding true the truth that air </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">isn’t</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> a natural kind, </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">then</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> you’ll hold it fixed.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">And it feels relevant that that auxiliary thing you need to hold true </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">is</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> true.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">And this phenomenon of being able to hold these things true in different ways, and also in a more agnostic way, matches the disjunctive examples that motivated the implication clause (e.g. you can hold ‘Hesperus is Phosphorus or my hat is on the table’ true without holding any particular disjunct true (agnostic case), or by holding the first disjunct true (as well as the second if you like) (ICI case), </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">or</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> by holding the first disjunct false and the second true (non-ICI case).</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">So it is possible that by accommodating this stuff in a different way, the implication clause would become superfluous. Which would be good, as otherwise excessive complexity threatens.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">As a rough first pass for </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">that</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> strategy, if we try to synthesize a concept covering the underlying things that you can hold true when you hold one of these tricky cases true in a non-agnostic way, we could use that. But note that it seems wrong to think of them </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">in general </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">as ‘supporting’ propositions, I think (which might otherwise have been a clue to how to characterize the notion we need). That sounds right for disjunctive cases and the Dylan/Zimmerman case, but </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">not</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> for the ‘Air is airy’ case. That doesn’t need support, I feel like saying. You can already fully know, off your own bat, that air is airy, while being agnostic about its natural kind status.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">The concept we need could be expressed with the phrase ‘counterfactual-invariance decider’. Since your holding these things true decides whether the proposition whose necessity is in question is counterfactually invariant for you or not. E.g. ‘Air is not a natural kind’ is a (positive) CI decider for ‘Air is airy’. ‘Hesperus is Phosphorus’ is a (positive) CI decider for ‘Hesperus is Phosphorus or my hat is on the table’ (and ‘Hesperus is not Phosphorus is a </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">negative</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> CI decider for it).</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">So, when we’re in ‘agnostic’ mode with respect to P we’re not holding true any of its CI deciders.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">This feels like good progress! So, maybe all the stuff about implication has been a dead end. What’s really going on is that we need to zero in on true CI deciders, and it just so happened in the disjunctive cases (and arguably in the Dylan/Zimmerman case given rich implication) that these implied the propositions in question. And there’s something nice about that, since we’ve seen Casullo make an analogous mistake: he thought </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">component propositions</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> were the key to the linking problem, and I <a href="http://sprachlogik.blogspot.com/2017/08/an-adventure-in-linking-necessity-to.html">thought I was very clever</a> to “realise” that it’s really implication. Now I’m thinking that may be wrong too, and the real, deep thing is CI-decidership. And it feels like this time this won’t turn out wrong. The notion is tailor-made!</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">So now, I think I can have a true account of necessity running something like:</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A proposition P is necessary iff it doesn’t vary across CSDs for which a true CI decider of P is held true.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Or perhaps we should simply say:</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">A proposition is necessary iff it has a true positive CI decider.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">(Note that this is now, unlike my old account which purported to give necessary and sufficient conditions for necessary </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">truth</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;">, an account of necessity (as in necessary truth </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">or</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> falsity). Note also that we can hold that propositions are often CI deciders for themselves - if positive, then they’re ICI. But ICI itself might no longer play a role in the analysis. There’s still a plausibly </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">a priori</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> element here too: given propositions P and Q (not necessarily distinct) it is </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">a priori</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> whether P is a CI decider of Q and, if it is, how it decides the matter. It’s also plausibly </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">a priori</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> whether a given proposition has a positive CI decider. What isn’t </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-style: italic; vertical-align: baseline;">a priori</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; vertical-align: baseline;"> in general is whether these propositions and their deciders are true.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I will try to investigate this further, and work on ways of clearly conveying and explaining the idea of a CI decider, and packaging the account as a whole. But I have a good feeling about it.</span></div><div id="UMS_TOOLTIP" style="background: transparent none repeat scroll 0% 0%; cursor: pointer; left: -100000px; position: absolute; top: -100000px; z-index: 2147483647;"></div>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-7083405175418147192017-09-04T19:03:00.000-07:002017-09-06T05:27:26.212-07:00Strohminger & Yli-Vakkuri Improve (in Some Respects) Upon Kipper's Bombshell (and My Account of Necessity May Be False)<i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">This post is quite compressed and relies on things explained in the&nbsp;<a href="http://sprachlogik.blogspot.com/2017/08/an-adventure-in-linking-necessity-to.html">previous</a>&nbsp;<a href="http://sprachlogik.blogspot.com/2017/08/kippers-bombshell.html">posts</a>&nbsp;on the task of linking necessity to apriority, as well as alluding to my account of necessity as expressed in&nbsp;<a href="https://sites.google.com/site/tristanhaze/Tristan%20Haze%20-%20Necessity%20and%20Propositions.pdf">my PhD thesis</a>. In a future post, I intend to explain and explore what these developments mean for my account of necessity.</span></i><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">There has recently appeared an unpublished manuscript on PhilPapers (PDF available&nbsp;<a href="https://philpapers.org/archive/YLIOAP.pdf">here</a>&nbsp;at time of writing) which contains even stronger counterexamples to both Casullo's and&nbsp;<a href="http://sprachlogik.blogspot.com/2017/08/an-adventure-in-linking-necessity-to.html">my proposed link</a>&nbsp;between necessity and apriority. It is by Margot Strohminger and Yuhani Yli-Vakkuri.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br />Strohminger &amp; Yli-Vakkuri argue that&nbsp;<a href="http://sprachlogik.blogspot.com/2017/08/kippers-bombshell.html">Kipper's</a>&nbsp;examples are contentious, relying on dubitable assumptions about natural kind terms and perhaps even embracing what they call 'Chalmersian two-dimensionalist ideology'. They provide even simpler examples of propositions whose general modal status cannot be known&nbsp;<i>a priori</i>&nbsp;(and, relevantly for me, these examples also don't seem to be&nbsp;<i>implied</i>&nbsp;by propositions whose general modal status can be known&nbsp;<i>a priori</i>). For example:</span><br /><blockquote class="tr_bq"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Bob Dylan is at least as tall as Robert Zimmerman.</span></blockquote><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">This is necessary, since Bob Dylan&nbsp;<i>is&nbsp;</i>Robert Zimmerman. But for all we can know&nbsp;<i>a priori</i>, Dylan and Zimmerman are distinct, in which case this proposition would not be necessary, but contingent.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But hold on a minute! My link appeals to implication, and I said that the example above isn't implied by a proposition whose general modal status is knowable <i>a priori</i>. But can't we say that it is implied by 'Bob Dylan is Robert Zimmerman', which we can know <i>a priori</i>&nbsp;to be necessary? Yes, we can - although here we need a notion of implication which takes into account the meaning of 'is at least as tall as' - or at least the fact that it's a certain kind of comparative expression - rather than just the meanings of subject-neutral particles like 'or', 'all' and 'some'. So, from the point of view of disproving Casullo's proposed link, this example may be the best available so, but from the point of view of disproving my proposed implication-involving link, Kipper's natural kind examples may still have an edge.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">It seems to be a very exciting time to be thinking about these issues! So far, in this post and the last, I've been talking about how these examples affect my proposed link between necessity and apriority. But the situation is more serious than that for me. The centrepiece of my PhD thesis was an account of the conditions under which a proposition is necessarily true (I've blogged about this account quite a bit here). And these developments, as far as I can tell, may well show that account to be false. This is very momentous for me, as I worked on that account for several years and considered it to be maybe my best bit of work.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I can't believe I didn't think of the example above in connection with my account! I even considered a very similar example when making a side point about using my notion of a genuine counterfactual scenario description (used in my account of necessity) to arrive at a definition of rigid designation which is in some ways more fundamental than the Kripkean one.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Stay tuned for more on whether and how these developments affect my account of necessity, and what can be done about it if they do.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com9tag:blogger.com,1999:blog-8137988136860941398.post-39631504289481181502017-08-30T19:40:00.000-07:002017-08-31T03:35:43.787-07:00Kipper's Bombshell<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">In a <a href="http://sprachlogik.blogspot.com/2017/08/an-adventure-in-linking-necessity-to.html">recent post</a> (and an article I am working on), I arrived at the view that if a proposition can be known to be necessary (i.e. necessarily true or false) then either it or its negation is in the deductive closure of a set of true propositions with <i>a priori </i>necessary character - i.e. propositions which are such that it can be known <i>a priori</i>&nbsp;that they are necessary.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">There is a <a href="https://philpapers.org/rec/KIPOWI">new article</a> by Jens Kipper forthcoming in <i>Analysis</i>, 'On what is apriori about necessities',&nbsp;which seems to make serious trouble for this view (as well as its ancestors). Here is the problem in my own words:</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Kipper zeroes in on the fact that with some terms, such as - plausibly - 'air' and 'water', it is not <i>a priori</i>&nbsp;whether they pick out a natural kind or not. It turns out that 'air' doesn't pick out a natural kind, and that 'water' does. Now, let 'airy' be a predicate that applies to a stuff when it exhibits the superficial characteristics that air has in our world, and similarly for 'watery'.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Kipper's bombshell is to point out that 'Air is airy' is plausibly necessary (since air doesn't have some underlying nature which makes it air - rather its being air is basically just a matter of its being airy) but 'Water is watery' is plausibly not necessary (since something with water's underlying nature, i.e. being comprised mainly of H20, could have existed in quite different conditions where it isn't watery). And it definitely seems like these things could not have been known <i>a priori</i>.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I have mixed feelings realising this. I was really happy with my proposed link between necessity and apriority. I still feel inclined to suppose that there is something in the idea. But I cannot deny the simplicity and insightfulness of Kipper's bombshell.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Kipper considers and casts serious doubt on a view that tries to escape the bombshell by claiming that meaning change occurs when we discover whether a term like 'air' doesn't pick out a natural kind. I am pretty sympathetic to Kipper's rebuttal of this, and am inclined to look elsewhere for a way of saving, or repairing, my link. Could I perhaps figure out a way of getting propositions which clearly do have <i>a priori</i>&nbsp;necessary character and which&nbsp;imply propositions like 'Air is airy'?</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I will post again on this matter once I get a better view of the situation.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-26301117559994327032017-08-23T22:46:00.002-07:002017-08-24T17:03:23.234-07:00Notes on Counterfactual Scenario Descriptions, Sources of Modal Error (or Uncertainty), and Deep Puzzles of Modality<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">One interesting thing about my <a href="https://sites.google.com/site/tristanhaze/Tristan%20Haze%20-%20Necessity%20and%20Propositions.pdf">account</a> of subjunctive necessity is the way it separates two kinds of things that we could be wrong or confused about in our judgements of subjunctive modality: the truth of what we're holding true for the purposes of a counterfactual scenario description (CSD) and the genuineness of that CSD.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br />For example, I might think 'Hesperus is not Phosphorus' is subjunctively possible because I falsely believe that Hesperus is Phosphorus. Or I might be acquainted with some strange animals I call Toves and then not feel sure whether 'Toves are animals' is necessary simply because I am not sure whether the things I am acquainted with are animals.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">By contrast, there are modal questions which do not centre - at least not in any definite way - on the truth or otherwise of what is being held true. For example, granting that I am human, could I have been an animal? Or how about a Neanderthal? Or a bank account?</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">And cosmic questions about whether there could have been less matter or energy, or perhaps just one atom in a void? And here the question arises: how do you know what you have to know in order to know whether something is necessarily the way it is or not? (In some cases, that seems clear. E.g. you have to know whether Hesperus is in fact Phosphorus in order to know whether it necessarily is. But in others it really doesn't.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Another puzzling thing stems from the way, in my account, you can have CSDs which aren't possible, since the things held true for them aren't true. For instance, if I think wrongly that Hesperus isn't Phosphorus (or even just grant that for the sake of argument), I will be prepared to produce CSDs involving Hesperus not being Phosphorus, and these may be perfectly genuine. This strikes me as an important virtue of my account - i.e., that it is some sort of advance, giving us a fruitful way of talking and thinking philosophically about modality. It is hard to say exactly why. One thing is that it enables us to bracket off distracting sources of modal uncertainty and error, perhaps allowing us to focus better on the stuff which really bothers us philosophically about modality.&nbsp;</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">In any case, this thing - about there being genuine CSDs which, despite being genuine, aren't possible because false things are held true for them - gives rise to some puzzlement in its own right. When we can go different ways on the question of whether Hesperus is Phosphorus or Clark Kent is Superman - questions of the identity or distinctness of things - it seems like our underlying way of thinking about things, our conceptual apparatus, is basically the same. And to a fair, but perhaps lesser extent, going different ways on the question of the underlying nature of cats, or Toves, or water also seems to leave our conceptual apparatus largely the same. (There may be something wrong or lacking in this description.) We get the sense that we can flip the switch either way on these things quite readily, and continue in much the same way in either case when it comes to grasping a range of genuine CSDs which arise on the assumption that things are the one way or the other. On the other hand, what of things which are - in a conceptual sense, I want to say - far from true?&nbsp;</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Things get puzzling very quickly once such questions come into view. If I somehow hold it true that humans are cats, can I then produce genuine CSDs according to which that is true? It is hard to know what to say. One thing is that there might be an issue about whether we can really hold such things true, or perhaps better, whether it makes sense to talk of holding such things true. But to that it may always be replied - OK, but we can sometimes <i>do something </i>here, in these cases where you might worry about whether we can really hold the things in question true or not.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Are there two ways, then, of getting out of the sphere of genuine CSD-hood? One by holding things true which are either true, or not a big deal or problematic to hold true, and then going further and further away from actuality, so to speak, until you say things we might hesitate to call CSDs (e.g. holding it true that I am human, but then talking about a scenario where I'm a cat), and another by holding far-out things true?</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Another worry concerns what might be called <i>modal encroachment</i>. The idea that, if we learn more about some things, we might realise that some things aren't possible that we thought were. And there is a question here about whether that could affect what we think about genuineness of a CSD, or whether what we formerly thought were not only genuine CSDs but possibilities (i.e. that the things being held true for those CSDs are the case) can always be retained as genuine CSDs by holding the right false things true.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I feel that with these issues my account, which could seem merely logic-choppy and perhaps trivial in a way, begins to make contact with some of the deeper puzzles surrounding modality.&nbsp;</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">In a future post I want to try to explore how our ideas might be prone to shifting and slipping without our realising it when we philosophize about modality. For instance, the obscure way the stakes can seemingly be raised in some way by the question of 'But could that really have happened?'. I also hope to make some progress on puzzles concerning 'whether the ground of modality is in us or the world', by trying to better uncover the thought processes underlying that unsatisfactory question. Perhaps then we will see better what the real issues are in this thicket of philosophy.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i>Postscript (or seedling for next time):</i></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i><br /></i></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Dim hypothesis re. Kripkean showing of necessity of identity: it shows that things couldn't have been otherwise in a deep way by showing that they couldn't have been otherwise in a shallow way.&nbsp;</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I.e. in a certain frame of mind, we might think 'What do we know about how, and the extent to which, things&nbsp;</span><i style="font-family: georgia, &quot;times new roman&quot;, serif;">really</i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">&nbsp;might have been different?'. A frame of mind with a sense of cosmic mystery, open to underlying system we have little or no inkling of. Then the Kripkean arguments come along and say 'Well, whatever the truth is about that, things certainly couldn't have been such that Hesperus isn't Phosphorus'.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">It is notable that Kripke's&nbsp;</span><i style="font-family: georgia, &quot;times new roman&quot;, serif;">results&nbsp;</i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">are necessities, or denials of possibility. This leaves it open that we have a way of thinking, or a concept of modality, on which all the Kripkean necessities are necessary as required, but where there is leeway which then disappears on some deeper view.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-10243928310142241162017-08-18T17:28:00.001-07:002017-08-18T17:28:43.178-07:00Scholarly Attention for the First Ever Sprachlogik Post!<span style="font-family: Georgia, Times New Roman, serif;">It recently came to my attention that the <a href="http://sprachlogik.blogspot.com/2011/02/liar-paradox-of-material-implication.html">first ever post</a> here, from back in 2011, is the subject of a <a href="https://philpapers.org/rec/MARTTF-5">journal article</a> by Matheus Silva, a Brazilian philosopher and logician.<br /><br />Silva has also recently <a href="https://philpapers.org/rec/SILIDO-5">engaged</a> with my <a href="https://philpapers.org/rec/HAZATB">argument</a> against the Brogaard-Salerno Stricture, a principle about when it is OK to reason using conditionals.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-27652604421403045312017-08-01T17:20:00.002-07:002017-08-30T20:46:05.204-07:00An Adventure in Linking Necessity to Apriority<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">There is an important link between necessity and apriority which can shed light on our knowledge of the former, but initially plausible attempts to spell out what it is fall victim to counterexamples. Casullo (2003) discusses one such proposal, argues that it fails, and suggests an alternative. In this post, I argue that Casullo’s alternative also fails, suggest another, argue that that fails too, and then suggest another which I hope is correct.</span><br /><i style="font-family: georgia, &quot;times new roman&quot;, serif;"><b><br /></b></i><i style="font-family: georgia, &quot;times new roman&quot;, serif;"><b>First proposal</b></i><br /><div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Kripke (1980) showed that it is not always knowable a priori whether a proposition is necessarily true. But, you might think, perhaps it is always knowable a priori whether a proposition has whatever truth value it has necessarily or contingently. To use Casullo’s (2003) terminology, while Kripke showed that knowledge of specific modal status (necessarily true, contingently false, etc.) is not always possible a priori, this leaves open the possibility of apriori knowledge of general modal status (necessary or contingent - and on this usage of ‘necessary’ and ‘contingent’, truth value is left open). Perhaps that is the link we are after between necessity and apriority.<br /><br />The claim that general modal status is always knowable a priori entails the following:<br /><br />(1) If <i>p</i> is a necessary proposition and S knows that <i>p</i> is a necessary proposition, then S can know a priori that <i>p</i> is a necessary proposition.</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br />(The second conjunct of (1)’s antecedent sidesteps the worry that some necessary propositions may be such that it is unknowable that they are necessary.)<br /><br />Casullo, following Anderson (1993), argues convincingly that this is false. Consider:</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br />(1X) Hesperus is Phosphorus or my hat is on the table.<br /><br />This is a necessary proposition, but for all any S could know a priori, it could be necessarily true (if the first disjunct is true), contingently true (if the first disjunct is false but the second true), or contingently false (if both disjuncts are false). So (1) can’t be right.</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i><b>Second proposal</b></i><br /><br />In an interesting effort to avoid the problem affecting (1), Casullo introduces the notions of conditional modal propositions and conditional modal status:</span><br /><blockquote class="tr_bq"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Associated with each truth functionally simple proposition is a pair of conditional propositions: one provides the specific modal status of the proposition given that it is true; the other provides its specific modal status given that it is false. Associated with each truth functionally compound proposition is a series of conditional propositions, one for each assignment of truth values to its simple components. Each conditional proposition provides the specific modal status of the proposition given that assignment of truth values. Let us call these propositions conditional modal propositions and say that S knows the conditional modal status of <i>p</i> just in case S knows all the conditional modal propositions associated with p. (Casullo (2003), p. 197.)</span></blockquote><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">His proposed link between necessity and apriority is as follows:<br /><br />(2) If <i>p</i> is a necessary proposition and S knows the conditional modal status of <i>p</i>, then S can know a priori the conditional modal status of <i>p</i>.<br /><br />Casullo dubs this ‘a version of the traditional account of the relationship between the a priori and the necessary that is immune to Kripke’s examples of necessary a posteriori propositions’ (Casullo (2003), p. 199). It handles (1X) nicely. Calling (1X)’s disjuncts ‘Hesp’ and ‘Hat’, its associated conditional modal propositions will run as follows:<br /><br />If Hesp is true and Hat is true, (1X) is necessary.<br />If Hesp is true and Hat is false, (1X) is necessary.<br />If Hesp is false and Hat is true, (1X) is contingent.<br />If Hesp is false and Hat is false, (1X) is contingent.<br /><br />These are plausibly knowable a priori, as required by (2). <br /><br />But consider:<br /><br />(2X) Everything is either such that it is either not Hesperus or is Phosphorus, or such that it is either on the table or not my hat.<br /><br />While it contains connectives, this is not a truth functional compound in the relevant sense, since it does not embed any whole propositions. So on Casullo’s proposal, (2X) will be associated with just a pair of conditional modal propositions. Which ones? A problem here is that there is no very clear positive case for any pair (the account, after all, was probably not formulated with (2X) in mind), but I think it is clear that the only candidate pair which could stand a chance is: <br /><br />If (2X) is true, it is necessary.<br />If (2X) is false, it is contingent.<br /><br />(After all, (2X) is true and necessary, so the other available choice for first member couldn’t be right, and the second member of the pair seems true and knowable a priori.)<br /><br />Instantiating Casullo’s proposal (2) on (2X), we get:<br /><br />If (2X) is a necessary proposition and S knows the conditional modal status of (2X), then S can know a priori the conditional modal status of (2X).<br /><br />But it seems clear that the first conditional modal proposition for (2X), i.e. that if (2X) is true, it is necessary, could not be known a priori. So (2) can’t be right either.<br /><br /><i><b>Third proposal</b></i><br /><br />What strikes one initially about the disjunctive counterexample to the first proposal is that it has a <i>component</i> whose general modal status is knowable a priori. But this isn’t true of the counterexample to the second proposal; it has no component propositions at all. What is true about both counterexamples is, not that they have cromponent propositions whose general modal status is knowable a priori, but that they are <i>implied</i> by such propositions.<br /><br />Let us say that a proposition <i>p</i> possesses a priori necessary character iff it can be known a priori that <i>p</i> is a necessary proposition, i.e. that <i>p</i> has whatever truth value it has necessarily. <br /><br />Now, I submit that if a proposition whose general modal status is knowable at all is necessarily true, then it is in the deductive closure of a set of true propositions possessing a priori necessary character.</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">How, though, to generalize this so that it covers all necessary propositions (i.e. necessarily false propositions as well as true ones)? For a few weeks, I thought this would work:</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">If a proposition whose general modal status is knowable at all is necessary, then it is either in the deductive closure of a set of true propositions possessing a priori necessary character, or it is in the deductive closure of a consistent set of false propositions possessing a priori necessary character.</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">To cast the point in a form similar to (1) and (2) above:</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br />(3) If <i>p</i> is a necessary proposition and S knows that <i>p</i> is a necessary proposition, then <i>p</i> is either in the deductive closure of a set of true propositions which S can know a priori to be necessary, or it is in the deductive closure of a consistent set of false propositions which S can know a priori to be necessary.<br /><br />But I have just recently realised that this is false as well.</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br />The problem lies with necessarily false propositions. Requiring consistency of the set of false propositions that implies a putative necessary proposition rules out necessarily false propositions that contradict themselves. E.g. 'It is both raining and not raining' is, and can be known to be, a necessary proposition, but it is not implied by any consistent set of false propositions of apriori necessary character. On the other hand, removing the consistency requirement causes the account to <i>over</i>generate, at least on a classical conception of implication; 'I had toast for breakfast' is implied by the set of false propositions of a priori necessary character {'2 + 2 = 4', 'not-(2 + 2 = 4)'}, since that set implies any proposition whatsoever.<br /><br /><i><b>Fourth proposal</b></i></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i><br /></i>Now, without wanting to rule out that we could specify a special implication-like relation which behaves as desired, I have nevertheless tentatively given up on bringing in consistency to get a general result which covers not only necessary true propositions but necessarily false ones as well. Instead, I think the thing to do is to exploit the idea that a necessarily false proposition's negation is necessarily true, giving us:<br /><br />(4) If <i>p</i> is a necessary proposition and S knows that <i>p</i> is a necessary proposition, then either <i>p</i> or its negation is in the deductive closure of a set of true propositions which S can know a priori to be necessary.<br /><br />Maybe <i>this</i> one is true! Please let me know, by comment or email, if you see a problem.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">[UPDATE 31/08/2017: <a href="https://sprachlogik.blogspot.com/2017/08/kippers-bombshell.html">Trouble has arisen</a>.]</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i>Thanks to Albert Casullo for helpful and encouraging correspondence on this topic.</i></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i><br /></i></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i><b>References</b></i><br /><br />Anderson, C. Anthony (1993). Toward a Logic of A Priori Knowledge. <i>Philosophical Topics</i> 21(2):1-20.<br /><br />Casullo, Albert (2003). <i>A Priori Justification</i>. Oxford University Press USA.<br /><br />Kripke, Saul A. (1980). <i>Naming and Necessity</i>. Harvard University Press.</span></div></div>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-34702013099643153672017-07-08T20:11:00.000-07:002017-07-09T00:40:07.310-07:00An Attempt to Diagnose the Disagreement over the Relational Explanation of Identity<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Here is what I have to say in response to <a href="http://sprachlogik.blogspot.com/2017/06/the-schmidentity-challenge-to-sui.html">the schmidentity challenge as posed to the <i>sui generis </i>view of identity statements</a>. (See also <a href="http://sprachlogik.blogspot.com/2012/03/identity-expressed-with-one-place.html">these</a> <a href="http://sprachlogik.blogspot.com/2013/01/notes-on-identity-and-idea-of-law-of.html">two</a> related posts from several years ago.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">OK, so we can grant that you can introduce a 'schmidentity' predicate in the way Kripke describes. We can also grant that this predicate could then get used to do what we do with identity statements. But can we, having granted these things, nonetheless deny that the meaning and function of identity statements is explained with the object-relation story?</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I am strongly inclined to do all of this. Why? Because the characteristic function of informative identity statements and their denials - the way they get us to merge and separate <i>mental files</i>, or <i>concepts of individuals </i>- is passed over in this explanation. Going along with the object-relation explanation seems to render this incidental, instead of the main point. That explanation makes it look as though the main function of an '<i>a </i>is <i>b</i>' statement is also fulfilled by the corresponding '<i>a </i>is<i> a</i>' statement, which of course it is not.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But, someone may argue, does the object-relation explanation <i>really</i> create this false appearance? And here it would be easy to be dogmatic. There would be something silly about insisting that yes, this sort of explanation really does create this false appearance. After all, my opponent - the philosopher who wants to say that the object-relation story is perfectly adequate, and that there's no problem here, and that anyone who thinks there is is in a muddle - doesn't actually seem to be confused about the fact that '<i>a</i> is <i>b</i>' statements are often useful in a way that the corresponding '<i>a</i> is <i>a</i>' statements are not. They would happily admit that. So the difference between us seems to be in whether we are happy to leave this out in our <i>primary explanation</i>, so to speak, of identity statements. </span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">And it is important that I allow that the object-relation explanation of identity statements does show something. It's not as if it is a sheer mistake. It shows that we can so to speak <i>depict</i> identity statements as a special case of relational statements, i.e. statements like 'John loves Mary'. I do not want to deny this, or deny that it is of philosophical interest.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">There is something<i> </i>neat or cool about this sort of observation, too. It has a charm to it, similar to the charm possessed by clever hacks (in the sense of computer culture). I think that the philosopher who wants to defend the object-relation story lacks a proper place to put this. They feel the charm, the strikingness, of the explanation, and - not wanting this to elude them - wrongly place it in the "primary explanation" place in their thinking, instead of a place marked something like "striking and potentially instructive thing you can say". So long as we only focus on the "primary explanation" place, it looks like the defender of the object-relation story is missing something and proposing something maddeningly objectionable, but it also looks like the antagonist of the object-relation story is missing something. It is not until we consider other possibilities for the significance of the object-relation story that we are able to give both parties their due.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">This, I now think, is a very important point (even though I may not have expressed it very well). I regret that I didn't manage to arrive at this point in my <a href="http://philpapers.org/rec/HAZOIS-2">paper</a> on this topic. I also think my predecessors were missing something in this regard.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">So, we can grant the possibility of the schmidentity predicate, and the possibility of it coming to be used to do the characteristic work of identity statements, but nonetheless deny that the object-relation story should take pride of place in our explanation of the meaning and function of identity statements. A leftover question here is: should we also deny that the meaning and function of statements made with the 'schmidentity' predicate, if they are being used in the way we use identity statements, is explained by their stipulated semantics? And the answer, I think, is Yes. If they are being used in that way, then the object-relation story should not take pride of place in their explanation. But it is understandable that we should hesitate here, since 'schmidentity' was introduced and defined by means of the object-relation story, and this invites us to look at their use - when they are being used in the characteristic way we use identity statements - as a kind of secondary thing, a happy side-effect.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(I feel like saying something more at this point, which may be more objectionable, about what other use (schm)identity statements may have, apart from their practical use which has to do with merging and separating. A metaphysical use, so to speak. And about what attitude we take to this use, or whether it might be a kind of illusion. And this relates to <a href="http://sprachlogik.blogspot.com/2013/01/notes-on-identity-and-idea-of-law-of.html">one of</a> the old posts linked to at the beginning. But I won't do more than make this hint, since these are treacherous waters and I wouldn't want to abuse the goodwill of a differently-minded reader.)</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-32706963660326938502017-06-10T20:02:00.000-07:002017-06-10T23:52:32.267-07:00The Schmidentity Challenge (to the Sui Generis View of Identity Statements)<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">In my (2016) I <a href="https://philpapers.org/rec/HAZOIS-2">defended</a> the idea that identity statements are <i>sui generis</i>. More precisely, I defended the idea that identity statements involving proper names (e.g. 'Hesperus is Phosphorus') are not to be explained by the claim that they ascribe a relation which holds between all objects and themselves and in no other case, or for that matter by the claim that they ascribe a relation between names (this latter claim being false). In contrast to my predecessors who railed against the object-relation view, I did not insist that the object-relation claim is <i>false</i> - I decided this was not a very clear thing to insist on, and anyway not really the point - but just that it doesn't explain the meaning and function of identity statements. It may be "something you can say", but it doesn't do that explanatory job. I thought, and still do think, that this is the way forward for the philosopher who feels that there is something fishy about the object-relation view, something which remains even if we succeed in avoiding - most likely by means of senses or similarly-motivated semantic difference-makers - the absurd conclusion that 'Hesperus is Hesperus' and 'Hesperus is Phosphorus' mean the same. </span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I defended my negative thesis about the explanation of identity statements against some possible objections in the paper, but one unaddressed challenge I have been thinking about in the years since writing the bulk of the paper (it took a long time to get it published, and I stopped trying for a while) is Kripke's celebrated 'schmidentity' argument. Here it is:</span><br /><blockquote class="tr_bq"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Suppose identity <i>were</i> a relation in English between the names. I shall introduce an artificial relation called 'schmidentity’ (not a word of English) which I now stipulate to hold only between an object and itself. Now then the question whether Cicero is schmidentical with Tully can arise, and if it does arise the same problems will hold for this statement as were thought in the case of our original identity statement to give the belief that this was a relation between the names. If anyone thinks about this seriously, I think he will see that therefore probably his original account of identity was not necessary, and probably not possible, for the problems it was originally meant to solve, that therefore it should be dropped, and identity should just be taken to the relation between a thing and itself. This sort of device can be used for a number of philosophical problems. (Kripke (1980), p. 108.)</span></blockquote><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">As you can see, the schmidentity argument is framed primarily as an argument against the name-relation view of identity statements, which I also argued against. But this argument also threatens my position. As I see it, the challenge is as follows. Kripke's schmidentity predicate is a term which is explicitly introduced - <i>explained</i>, it is natural to say - as ascribing a relation which holds between all objects and themselves and in no other case. So, whatever is true of identity statements, <i>schmidentity</i> statements <i>can</i> be - indeed <i>have been</i> - explained by means of the object-relation stuff which I wanted to say fails to explain the meaning of identity statements. But schmidentity statements could be used to do what we do with identity statements. So then what grounds have we for supposing that identity statements differ semantically from schmidentity statements? Perhaps none. But then if identity statements and schmidentity statements are semantically on a par, and the latter can (are) explained by the object-relation stuff, then so can the former. So now it looks like my position is wrong.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I think this is a serious challenge to my position (about the object-relation claim not being explanatory of identity statements), but I can't help feeling that it misses something and that my position is right in some way. I will try to respond to the challenge in my next post here.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><b><i>References</i></b></span><br /><br /><div class="export"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"> Haze, Tristan (2016). On Identity Statements: In Defense of a <i>Sui Generis</i> View. <i class="pubName">Disputatio</i> 8 (43):269-293.</span></div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"> Kripke, Saul A. (1980). <i>Naming and Necessity</i>. Harvard University Press.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-60647667687779651422017-05-06T20:47:00.000-07:002017-08-24T17:03:41.167-07:00The Pre-Kripkean Puzzles are Back<div style="text-align: right;">Yes, but does Nature have no say at all here?! Yes.</div><div style="text-align: right;">It is just that she makes herself heard in a different way.</div><div style="text-align: right;">Wittgenstein (MS 137).</div><div style="text-align: left;"><br /></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: left;"><span style="background-color: transparent; color: black; font-style: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Modality was already puzzling before Kripke - there’s a tendency for the potted history of the thing to make it seem like just before Kripke, philosophers by and large thought they had a good understanding of modality. But there were deep problems and puzzles all along, and I think many were alive to them.</span></span></div><div style="text-align: left;"><b style="font-weight: normal;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></b></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: left;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">There is a funny thing about the effect of Kripke’s work which I have been starting to grasp lately. It seems like it jolted people out of certain dogmas, but that the problems with those dogmas were actually already there. The idea of the necessary </span><span style="background-color: transparent; color: black; font-style: italic; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">a posteriori</span><span style="background-color: transparent; color: black; font-style: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> sort of stunned those ways of thinking. But once the dust settles and we learn to factor out the blatantly empirical aspect from subjunctive modality - two main ways have been worked out, more on which in a moment - the issue comes back, and those ways of thinking and the problems with them are just all still there.</span></span></div><div style="text-align: left;"><b style="font-weight: normal;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></b></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: left;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">(When I was working on my <a href="https://sites.google.com/site/tristanhaze/Tristan%20Haze%20-%20Necessity%20and%20Propositions.pdf">account</a> of subjunctive necessity </span><span style="background-color: transparent; color: black; font-style: italic; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">de dicto</span><span style="background-color: transparent; color: black; font-style: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, I thought of most pre-Kripkan discussions of modality as irrelevant and boring. Now that I have worked that account out, they are seeming more relevant.)</span></span></div><div style="text-align: left;"><b style="font-weight: normal;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></b></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: left;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">What are the two ways of factoring out the aposterioricity of subjunctive modality? There is the two-dimensional way: construct “worlds” using the sort of language that doesn’t lead to necessary </span><span style="background-color: transparent; color: black; font-style: italic; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">a posteriori</span><span style="background-color: transparent; color: black; font-style: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> propositions, and then make the truth-value of subjunctive modal claims involving the sort of language that does lead to them depend on which one of the worlds is actual.</span></span></div><div style="text-align: left;"><b style="font-weight: normal;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></b></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: left;"><span style="background-color: transparent; color: black; font-style: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">This is currently the most prominent and best-known approach. However, it involves heady idealizations, many perplexing details, and various questionable assumptions. I think the difficulty of the two-dimensional approach has kept us in a kind of post-Kripkean limbo for a surprisingly long time now. Except perhaps in a few minds, it has not yet become very clear how the old pre-Kripkean problems are still lying in wait for us. I have hopes that the second way of factoring out will move things forward more powerfully (while I simultaneously hope for a clearer understanding of two-dimensionalism).</span></span></div><div style="text-align: left;"><b style="font-weight: normal;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></b></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: left;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">What is the second way? It is to observe that the subjunctively necessary propositions are those which are members of the deductive closure of the propositions which are both true and C, where C is some </span><span style="background-color: transparent; color: black; font-style: italic; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">a priori</span><span style="background-color: transparent; color: black; font-style: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> tractable property. (On my account of C-hood, the closure version of the analysis is equivalent to the somewhat easier to understand claim that a proposition is necessary iff it is, or is implied by, a proposition which is both C and true. On Sider’s account of C-hood this equivalence fails.)</span></span></div><div style="text-align: left;"><b style="font-weight: normal;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></b></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: left;"><span style="background-color: transparent; color: black; font-style: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">My account of subjunctive necessity explains condition C as inherent counterfactual invariance, which in turn is defined using the notion of a genuine counterfactual scenario description. And it is with these notions that the old-style puzzles come back up. Sider’s account has it that C-hood is just a conventional matter - something like an arbitrary, disjunctive list of kinds of propositions. (Here we get a revival of the old disagreements between conventionalists and those who were happy to explain modality semantically, but suspicious of conventionalism.) </span></span></div><div style="text-align: left;"><b style="font-weight: normal;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></b></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: left;"><span style="background-color: transparent; color: black; font-style: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">What are these returning puzzles all about? They are about whether, and in what way, meaning and concepts are arbitrary. And about whether, and in what way, the world speaks through meaning and concepts. Hence the quote at the beginning, and the quote at the end of <a href="http://sprachlogik.blogspot.com/2017/04/reflections-on-my-claim-that-inherent.html">this companion post</a>.</span></span></div>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-67954988620811588392017-05-02T21:13:00.000-07:002017-05-11T06:23:00.150-07:00On Warren's 'The Possibility of Truth by Convention'<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Recently I read Jared Warren's '<a href="https://philpapers.org/rec/WARTPO-32">The Possibility of Truth by Convention</a>'. Sometimes when I read a paper, I strongly suspect I will end up finding it wrong-headed, and accordingly go in with a spot-the-fallacy attitude. I confess I did this in this case, but as I read it my attitude changed. Having read it, I now think I have had a prejudice against conventionalist ideas. And this makes sense: I have been trying to develop an <a href="https://sites.google.com/site/tristanhaze/Tristan%20Haze%20-%20Necessity%20and%20Propositions.pdf">analysis</a> of subjunctive necessity <i>de dicto</i>, and an <a href="http://sprachlogik.blogspot.com/2017/04/explaining-a-priori-in-terms-of-meaning.html">explanation of apriority</a>, which appeal crucially to considerations I have been <a href="http://sprachlogik.blogspot.com/2017/04/reflections-on-my-claim-that-inherent.html">thinking of as broadly semantic</a>. And one important defensive point for me has been that this does not entail conventionalism of any kind. I still think that's true, and still think it's important to point out since many philosophers are dead against conventionalism, but I think getting used to making that defensive point has led me to underestimate conventionalism. I may not agree with it (I suppose I'm agnostic now), but Warren's paper has helped me to see that there is more to it than I had been willing to allow.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Still, there is a point late in the argument that I have an issue with. In this post I will briefly summarize the key moves in Warren's argument and then raise this issue.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Warren discusses a widely adhered-to 'master argument' against conventionalism which runs as follows. The basic idea behind it is that truth by convention is a confused idea because, while conventions may make it the case that a sentence expresses the particular proposition is does, conventions cannot make the proposition itself true (unless it's itself about conventions).</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><u><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Master Argument:</span></u><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">P1. Necessarily, a sentence S is true iff (<i>p</i>&nbsp;is a proposition &amp; S means <i>p</i>&nbsp;&amp; <i>p </i>is the case).</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">P2. It's not the case that linguistic conventions make it the case that <i>p</i>.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">C. Therefore, it's not the case that linguistic conventions make it the case that S is true.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Warren points out that 'making it the case that' admits of different readings. One is metaphysical, as in truthmaker theory. Another is causal, as in 'causes it to be the case that'. But another is explanatory, as in 'explains why it is the case that'. This explanatory reading, Warren contends, is what real conventionalism should be understood as working with. And, Warren argues convincingly, the argument isn't valid on that reading, since explanatory 'makes it the case that' contexts are hyperintensional: if you take a sentence embedded in such a context and substitute for it a sentence which is intensionally equivalent, you sometimes change the truth-value of the sentence it was embedded in. Warren's illustrative example:</span><br /><blockquote class="tr_bq"><span style="background-color: white; color: #2a2a2a; font-size: 16px;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">[I]t is true that God's decree of ‘let there be light’ made it the case that (in the relevant sense) light exists, but it is false that either 2&nbsp;+ 2&nbsp;=&nbsp;5 or God decreeing ‘let there be light’ made it the case that (in the relevant sense) light exists.</span></span></blockquote><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">So, the Master Argument isn't valid on the explanatory reading of 'make it the case that'. But can't this be patched up? As Warren notes:</span><br /><blockquote class="tr_bq"><span style="background-color: white; color: #2a2a2a; font-size: 16px;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">if proponents of the argument accept a special principle requiring that explanations of sentential truth must also explain why the proposition expressed obtains, then a modified version of the master argument can be mounted that doesn't assume the intensionality of explanatory contexts.</span></span></blockquote><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Warren considers the prospects of shoring up the Master Argument with the principle he calls Propositional Explanation:</span><br /><blockquote class="tr_bq"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><em style="background-color: white; border: 0px; box-sizing: border-box; color: #2a2a2a; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Propositional</em><span style="background-color: white; color: #2a2a2a; font-size: 16px;">&nbsp;</span><em style="background-color: white; border: 0px; box-sizing: border-box; color: #2a2a2a; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">explanation</em><span style="background-color: white; color: #2a2a2a; font-size: 16px;">&nbsp;: If Δ (explanatorily) makes it the case that sentence&nbsp;</span><em style="background-color: white; border: 0px; box-sizing: border-box; color: #2a2a2a; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">S</em><span style="background-color: white; color: #2a2a2a; font-size: 16px;">&nbsp;is true, then Δ (explanatorily) makes it the case that&nbsp;</span><em style="background-color: white; border: 0px; box-sizing: border-box; color: #2a2a2a; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">p</em><span style="background-color: white; color: #2a2a2a; font-size: 16px;">&nbsp;(where&nbsp;</span><em style="background-color: white; border: 0px; box-sizing: border-box; color: #2a2a2a; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">p</em><span style="background-color: white; color: #2a2a2a; font-size: 16px;">&nbsp;is a proposition and&nbsp;</span><em style="background-color: white; border: 0px; box-sizing: border-box; color: #2a2a2a; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">S</em><span style="background-color: white; color: #2a2a2a; font-size: 16px;">&nbsp;means that&nbsp;</span><em style="background-color: white; border: 0px; box-sizing: border-box; color: #2a2a2a; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">p</em><span style="background-color: white; color: #2a2a2a; font-size: 16px;">).</span>&nbsp;</span></blockquote><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But Warren argues that the conventionalist has no good reason to accept this, and that it comes out of a way of thinking about the philosophy of language - he uses the phrase 'meta-semantic picture' - which they 'can, do, and should reject' (which makes the anti-conventionalist argument pretty weak). On the way of thinking Warren has in mind, propositions are in some sense more fundamental, and the truth of sentences is in some sense derivative of the truth of propositions.&nbsp;</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Now, I am happy to agree that conventionalists 'can, do, and should reject' this sort of picture of the philosophy of language. But I am not so sure that they should therefore deny Propositional Explanation. Maybe they can (and even should) accept Propositional Explanation, <i>not </i>because propositions come first in the order of explanation, but because - on their picture - once you've explained the truth of a sentence, you get an explanation of the truth of the proposition it expresses "for free". They can still block the Master Argument, however, by&nbsp;<i>denying P2</i>.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(Note in this connection that we should arguably separate two uses of 'the case' in this discussion. In the first premise of the Master Argument -&nbsp;</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">P1. Necessarily, a sentence S is true iff (</span><i style="font-family: georgia, &quot;times new roman&quot;, serif;">p</i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">&nbsp;is a proposition &amp; S means&nbsp;</span><i style="font-family: georgia, &quot;times new roman&quot;, serif;">p</i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">&nbsp;&amp;&nbsp;</span><i style="font-family: georgia, &quot;times new roman&quot;, serif;">p&nbsp;</i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">is the case).</span></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">- 'is the case', for the argument to work against&nbsp;<i>truth&nbsp;</i>by convention,&nbsp;should be read as 'true'. But in the second premise -&nbsp;</span></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">P2. It's not the case that linguistic conventions make it the case that&nbsp;</span><i style="font-family: georgia, &quot;times new roman&quot;, serif;">p</i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">.</span></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">- the second 'the case' is part of the phrase 'makes it the case that' which, Warren argues, is intended by the conventionalist to pick out an explanatory relation. And here we're really talking about making it the case, in this sense, that a proposition is&nbsp;<i>true -&nbsp;</i>and this gets passed over&nbsp;if we just write 'makes it the case that&nbsp;<i>p</i>'.)</span></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Now, on my suggestion, the conventionalist's&nbsp;<i>reason</i>&nbsp;for accepting Propositional Explanation would be anathema to the anti-conventionalist for whom propositions are more fundamental, just as the anti-conventionalist's reason is anathema to the conventionalist. But maybe they can (and even should) agree on Propositional Explanation itself. This doesn't leave the conventionalist in much of a pickle, since they can - instead of trying to deny Propositional Explanation - just hammer their explanatory reading of 'makes it the case that' and use <i>that</i>&nbsp;to deny P2, arguing that P2 may be right if 'makes it the case that' is read metaphysically or causally, but that it is false on their intended reading.</span><br /><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Why doesn't Warren suggest going this way? His reasons are suggested in these passages:</span><br /><blockquote class="tr_bq"><span style="background-color: white; color: #2a2a2a; font-size: 16px;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(...) a version of conventionalism about arithmetical truth might maintain that the truth of ‘2&nbsp;+ 2&nbsp;=&nbsp;4’is fully explained by our linguistic conventions while also thinking that a full explanation of why 2&nbsp;+ 2&nbsp;=&nbsp;4 is a matter internal to mathematics and therefore should appeal to mathematical facts rather than linguistic facts.</span></span></blockquote><span style="background-color: white; color: #2a2a2a;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">And:&nbsp;</span></span><br /><blockquote class="tr_bq"><span style="background-color: white; color: #2a2a2a; font-size: 16px;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Premise (2) will be justified by some argument to the effect that it would be extremely odd and implausible to think that our linguistic conventions could fully explain why 2&nbsp;+ 2&nbsp;=&nbsp;4 (e.g.), since this will be true in languages with markedly different linguistic conventions than our own and would have been the case even if our linguistic conventions had never existed.&nbsp;</span></span></blockquote><span style="background-color: white; color: #2a2a2a;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Wanting to allow for these points seems to make Warren think conventionalists should deny Propositional Explanation. But note that the above points are about 'why 2&nbsp;+ 2 = 4', i.e., not about why some proposition has some status. So for these points to support Propositional Explanation, propositions have to be thought of as having a very close metaphysical relationship to states of affairs (whose explanations, if they are mathematical states of affairs for instance, should be internal to mathematics). But it seems to me that that&nbsp;way of thinking about propositions is anathema to the conventionalist, who instead should see them as a kind of abstraction from sentences and our uses of them. That is why they can accept Propositional Explanation on the grounds that once you've explained the truth of a sentence you get an explanation of the truth of its expressed proposition "for free". And that is why they can deny P2.</span></span><br /><span style="background-color: white; color: #2a2a2a; font-size: 16px;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">So, the latter part of Warren's argument seems, if I'm reading him right, to be that the conventionalist, after defending themselves against the Master Argument by pointing out that they intend an explanatory reading of 'makes it the case that' on which that argument is invalid, should go on to respond to the <i>modified </i>Master Argument by protesting that it rests on a view, Propositional Explanation<i>,</i>&nbsp;which is anathema to their approach to the philosophy of language. But I suspect that it may be better for them to embrace Propositional Explanation - not because propositions are more fundamental in some way that their opponents think they are, but because if you explain the truth of a sentence, you get an explanation of the truth of the expressed proposition "for free" - and instead deny P2, which is anathema to their approach to the philosophy of language.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">The conventionalist can hold that the Master Argument is invalid <i>and</i>&nbsp;that it rests on a false premise, and that the modified Master Argument, i.e. the Master Argument augmented with Propositional Explanation, is valid but unsound, <i>not </i>because Propositional Explanation is false, but&nbsp;because of the false premise that the plain Master Argument also contained.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">This is of course not a fundamental disagreement with Warren's overall project here. In a broad sense, I am working alongside Warren and trying to give the conventionalist more options (something I am surprised to find myself doing!). If I have a disagreement with Warren here, it is about which option is best for them.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Reference</span></i><br /><i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: white; color: #333333;">Warren, Jared (2014). The Possibility of Truth by Convention.&nbsp;</span><em class="pubName" style="background-color: white; box-sizing: border-box; color: #333333;">Philosophical Quarterly</em><span style="background-color: white; color: #333333;">&nbsp;65 (258):84-93.</span></span><br /><br />Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-18266920564985088482017-04-21T19:54:00.001-07:002017-04-21T21:39:46.518-07:00Explaining the A Priori in Terms of Meaning and Essence<span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">It wasn't just the positivists who thought there was a tight connection between meaning and truth in the case of <i>a priori</i> propositions:</span></span><br /><blockquote class="tr_bq"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-size: small;"><span id="docs-internal-guid-c7e34908-8fb7-74de-d373-44876aa6cf59" style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">However, it seems to me that nevertheless one ingredient of this wrong theory of mathematical truth [i.e. conventionalism] is perfectly correct and really discloses the true nature of mathematics. Namely, it is correct that a mathematical proposition says nothing about the physical or psychical reality existing in space and time, because it is true already owing to the meaning of the terms occurring in it, irrespectively of the world of real things. What is wrong, however, is that the meaning of the terms (that is, the concepts they denote) is asserted to be something man-made and consisting merely in semantical conventions. (Gödel (1951/1995), p. 320.)</span></span></span></blockquote><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Perhaps we should try to recover some insight from the idea, nowadays highly unfashionable within philosophy (but alive and well in the broader intellectual culture, I think), that <i>a priori</i> truths like those of mathematics are in some sense true owing to their meanings. Philosophers often used to express this by calling such propositions 'necessarily true', but since Kripke that sort of usage has been crowded out by another.</span></span></span><br /><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">&nbsp;</span></span></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-size: small;">&nbsp;</span></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-size: small;">Noteworthy in this connection is that Kripke was not altogether gung ho about his severance of necessity from apriority:</span></span><br /><blockquote class="tr_bq"><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span id="docs-internal-guid-c7e34908-8fa4-27e4-6206-461b508ba6f2" style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">The case of fixing the reference of ‘one meter’ is a very clear example in which someone, just because he fixed the reference in this way, can in some sense know </span><span style="background-color: transparent; color: black; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">a priori </span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">that the length of this stick is a meter without regarding it as a necessary truth. Maybe the thesis about a prioricity implying necessity can be modified. It does appear to state some insight which might be important, and true, about epistemology. In a way an example like this may seem like a trivial counterexample which is not really the point of what some people think when they think that only necessary truths can be known </span><span style="background-color: transparent; color: black; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">a priori</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">. Well, if the thesis that all </span><span style="background-color: transparent; color: black; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">a priori</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> truth is necessary is to be immune from this sort of counterexample, it needs to be modified in some way. [...] And I myself have no idea it should be modified or restated, or if such a modification or restatement is possible. (Kripke (1980), p. 63.)</span></span></span></blockquote><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">This may make it sound like the required modification would consist in somehow ruling out the problematic contingent <i>a priori</i> truths from the class of truths whose epistemic status is to be explained. But Chalmers' idea of the <a href="http://consc.net/papers/tyranny.html">tyranny of the subjunctive</a> suggests another route: try instead to find a different notion of necessity - indicative, as opposed to subjunctive, necessity; truth in all worlds considered as actual, rather than truth in all worlds considered as counterfactual - better suited to the explanation of apriority.</span></span></span><br /><br /><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Now, in Chalmers' epistemic two-dimensionalist framework, indicative necessity is itself explained in epistemic terms. But if we try for a more full-bloodedly semantic conception of it, we may get something more explanatory of the special epistemic status of <i>a priori</i> truths. The notion we are after is something like: a proposition is indicatively necessary iff, given its meaning, it <i>cannot but</i> be true. And the modality here is not supposed to be epistemic.</span></span></span><br /><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><br /></span></span></span><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">But what aspect of its meaning? Sometimes 'meaning' covers relationships to things out in the world, and even the things out there themselves. What we are interested in is <i>internal</i> meaning. Putnam's Twin Earth thought experiment - though this is not how he used it - lets us see the distinction we need here. We want to talk about meaning in the sense in which Earth/Twin Earth pairs of propositions mean the same. This can be articulated using the middle-Wittgenstein idea of the role an expression plays in the system it belongs to (see Wittgenstein (197<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">4<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">, Part I))</span></span>.</span></span></span><br /><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><br /></span></span></span><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">So, what if we say that a proposition is indicatively necessary iff any proposition with its internal meaning <i>must</i>, in a non-epistemic sense, be true? Can indicative necessity in <i>this</i> sense be used to explain apriority?</span></span></span><br /><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><br /></span></span></span><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Maybe not, since there are indicatively necessary truths which are indicatively necessary only because their instantiation requires their truth. Example: language exists. (Language is here understood as a spatiotemporal phenomenon.) This is indicatively necessary, because any proposition with its internal meaning must be true, if only because the very existence of that proposition requires it to be true. Its truth comes about from the preconditions for its utterance, but - you might think - not from the internal meaning itself. It is interesting to note that it is indicatively necessary, but it lacks the special character of </span><span style="background-color: transparent; color: black; font-weight: 400; text-decoration: none; vertical-align: baseline;"><i>a priori</i>&nbsp;propositions whereby they, in some sense, don't place specific requirements on the world.</span></span></span><br /><br /><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">This situation pattern-matches with Fine's celebrated (1994) <a href="http://philosophy.fas.nyu.edu/docs/IO/1160/essence.pdf%2F1160%2Fessence.pdf">distinction</a> between necessary and essential properties. Socrates is necessarily a member of the set {Socrates}, but that membership is not part of his essence, since it doesn't have enough to do with Socrates as he is in himself. Likewise, he is necessarily distinct from the Eiffel Tower, but this is no part of his essence. So let us throw away the ladder of indicative necessity and instead hone in on the notion of <i>essential truth</i>. A proposition is essentially true iff it is of its internal meaning's essence to be true (i.e. to be the internal meaning of a true proposition).</span></span></span><br /><br /><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Thus, with encouragement from&nbsp;</span></span></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Gödel</span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">&nbsp;and Kripke, we can develop ideas from Chalmers, Putnam, Wittgenstein, and Fine, to yield:</span><br /><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><br /></span></span></span><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">To say that a proposition is <i>a priori</i> is to say that it can, in some sense, be known independent of experience. (You may need experience to get the concepts you need to understand the proposition, but you don't need any particular further experience to know that the proposition is true.) What is distinctive about these propositions which <span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">explains their being<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"> knowable </span></span>in that peculiar way? It is that their internal meanings - their roles in language - are, of their very essence, the internal meanings of true propositions; any proposition with that internal meaning <i>must </i>be true, and not for transcendental reasons relating to the pre-conditions of the instantiation of the proposition, but as a result of that internal meaning in itself.</span></span></span><br /><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><br /></span></span></span><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">So we can have an account of apriority which explains it in terms of a tight connection between meaning and truth, freed of its accidental associations with conventionalist and deflationary views about meaning, modality and essence.</span></span></span><br /><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><br /></span></span></span><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-weight: 400; text-decoration: none; vertical-align: baseline;">This is not to say that </span></span></span><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-weight: 400; text-decoration: none; vertical-align: baseline;"><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><i>a priori</i></span></span></span> propositions' truth is to be explained in a case by case way by considerations about meaning and essence. That would be to crowd out the real mathematical justifications of non-trivial mathematical truths. But explaining apriority in general in this way wards off misunderstandings which come from treating <i>a priori</i> truths too much like empirical truths. And that is what makes it an explanation.</span></span></span><br /><br /><b><i><span style="font-size: small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-weight: 400; text-decoration: none; vertical-align: baseline;">References</span></span></span></i></b><br /><br /><span style="font-size: x-small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: white; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Chalmers, David J. (1998). The tyranny of the subjunctive.</span><span style="background-color: white; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> (unpublished)</span></span></span><br /><br /><span style="font-size: x-small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: white; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Fine, Kit (1994). Essence and modality. </span><span style="background-color: white; color: black; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Philosophical Perspectives</span><span style="background-color: white; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> 8:1-16.</span></span></span><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: x-small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: white; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">G</span></span></span><span style="font-size: x-small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: white; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">ö</span>del, Kurt (1951/1995). Some basic theorems on the foundations of mathematics and their implications. In Solomon Feferman (ed.), </span><span style="background-color: white; color: black; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Kurt Gödel, Collected Works</span><span style="background-color: white; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">. Oxford University Press 290-304. (Originally delivered on 26 December 1951 as the 25th annual Josiah Willard Gibbs Lecture at Brown University.)</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">&nbsp;</span></span></span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><br /><span style="font-size: x-small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Kripke, Saul A. (1980).</span><span style="background-color: transparent; color: black; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> Naming and Necessity</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">. Harvard University Press.</span></span></span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><br /><span style="font-size: x-small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Putnam, Hilary (1973). Meaning and reference. </span><span style="background-color: transparent; color: black; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Journal of Philosophy</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> 70 (19):699-711.</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">&nbsp;</span></span></span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><br /><span style="font-size: x-small;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Wittgenstein, Ludwig (1974). </span><span style="background-color: transparent; color: black; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Philosophical Grammar</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">. University of California Press.</span></span></span></div><div id="UMS_TOOLTIP" style="background: transparent none repeat scroll 0% 0%; cursor: pointer; left: -100000px; position: absolute; top: -100000px; z-index: 2147483647;"></div>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-89325971391200334812017-04-21T05:54:00.000-07:002017-04-21T06:36:58.181-07:00Modern Quantificational Logic Doesn't Subsume Traditional Logic<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">It seems to be a received view about the relationship of traditional Aristotelian logic to modern quantificational logic that the inferences codified in the old-fashioned syllogisms - All men are mortal, Socrates is a man, etc. - are all, in some sense, subsumed by modern quantificational logic. (I know I have tended to assume this.)</span><br /><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But what about:</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">P1. All men are mortal.</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">C. Everything is such that (it is a man&nbsp;<span id="docs-internal-guid-97b0c372-9074-b343-09f0-79348d88f868"><span style="font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">⊃</span></span>&nbsp;it is mortal)? &nbsp;</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">This is a logical inference. It is not of the form 'A therefore A'. It embodies a very clever logical discovery! P1 and C are not the same statement. Talk of 'translating' the former by means of the latter papers over all this.</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Modern quantificational logic does not really capture the inferences captured by traditional logic, any more than it captures this link between the two. It does capture inferences which, given logical insight, can be seen to parallel those codified by traditional logic, but that is not the same thing.</span></div>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com1tag:blogger.com,1999:blog-8137988136860941398.post-62295960979701798702017-04-03T23:27:00.001-07:002017-04-09T18:58:12.765-07:00Reflections on My Claim that Inherent Counterfactual Invariance is Broadly Semantic<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><i>This post presupposes knowledge of my account of subjunctive necessity </i>de dicto<i>&nbsp;as expressed in my <a href="https://sites.google.com/site/tristanhaze/Tristan%20Haze%20-%20Necessity%20and%20Propositions.pdf">thesis</a> and in a paper derived from it which I have been working on. (I hope my self-criticism here doesn't cause any should-have-been-blind referees to reject the paper. A revise-and-resubmit verdict I could live with.) Here I try to take a next step in getting clear about the status and significance of the account.</i></span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; white-space: pre-wrap;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; white-space: pre-wrap;">In my </span><a href="https://sites.google.com/site/tristanhaze/Tristan%20Haze%20-%20Necessity%20and%20Propositions.pdf" style="font-family: georgia, &quot;times new roman&quot;, serif; font-size: 11pt; white-space: pre-wrap;">thesis</a><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; white-space: pre-wrap;"> and derived paper, I propose that a proposition is necessary iff it is, or is implied by, a proposition which is both inherently counterfactually invariant (ICI) and true, and explicate this notion of ICI.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; white-space: pre-wrap;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; white-space: pre-wrap;">I claim that ICI is broadly semantic, and put this forward as a key motivation and virtue of the account. I don’t provide much argument for this claim - the intention, I suppose, was that this would just seem self-evident. But I have become increasingly aware of the importance of the fact that this could be challenged, and the importance of getting clearer about the underlying primitive notion of a genuine counterfactual scenario description (CSD).</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">I do provide one reason, near the end of my presentation of my account, for thinking that ICI is broadly semantic </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">given my preferred approach to propositions and meaning</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">. But there are two reasons for wanting more. One is that it may be hoped that my claim that ICI is broadly semantic could be justified independently of my particular approach to propositions and meaning, where I advocate understanding what I distinguish as the ‘internal’ component of meaning as </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">role in language system</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">. A second, perhaps more suggestive, reason for wanting more is that, even given my preferred approach, the argument I give is basically this: ICI is explained in terms of how a proposition - its negation, really - behaves in certain contexts - namely CSDs. But here of course I have to single out </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">genuine </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">CSDs.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">And here’s the thing. (At least, the following seems to be right.) For my claim that ICI is broadly semantic to hold water, the notion of </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">genuineness</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"> of a CSD had better be broadly semantic. For it is not enough for a notion to be broadly semantic that it can be characterized in terms of appearance in certain sorts of linguistic context C, where C-hood is blatantly extra-semantic. For instance, we may say a proposition has G iff it (or its negation, to make this more like the ICI case) doesn’t appear in any description which has the property of being written in some notebook I have in my room. In that case, it is plain that whether or not a proposition has G is </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">not</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"> a matter of its meaning or nature.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">So, I now think that the little argument I give at the end of my presentation of my account, about how my particular approach to propositions and meaning ‘fits well’ with the notion of ICI as broadly semantic only goes so far, and that as an argument that given my particular approach the notion of ICI </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">is</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"> or </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">should be</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"> seen as broadly semantic, it is weak, since it gives no reason to think that the all-important notion of genuineness of CSD is broadly semantic.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; white-space: pre-wrap;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; white-space: pre-wrap;">Further, I think it is clear that I want to put forward my account, and I think the account has theoretical value, independent of whether a case can be made that genuineness of CSD is broadly semantic. And so my whole presentation of why my account is interesting and of its motivation is somewhat crude. As a story about what caused it, and the specific things I was thinking, it may have some interest. But as a way of situating the theory and giving a sense of what its value (within philosophy) consists in, it is crude and not really to the point. I do of course hint at other sources of interest</span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-size: 11pt; white-space: pre-wrap;"> </span><span style="font-size: 11pt; white-space: pre-wrap;">(e.g. that the account clarifies the relationship between the notion of necessity and those of truth and implication)</span></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; white-space: pre-wrap;">, and don’t rest everything on the ‘semantic hunch’, but I do perhaps give it too prominent a place - or at least, an incompletely justified place.</span><br /><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"><br /></span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">So, </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">is </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">the notion of a ‘genuine counterfactual scenario description’ broadly semantic? And what does it mean to be broadly semantic? I may follow up with a post addressing these questions more thoroughly, but for now a couple of remarks. Whatever it is to be broadly semantic, it is not to be </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">conventional</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"> in any sense. The idea is perhaps better gotten at, in some ways, by saying that genuine CSD-hood is a </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">conceptual</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"> matter. But really I need to roll up my sleeves and investigate this more closely - it is not merely a question of hitting on some formulation. Finally, I propose that the following passage from §520 of Wittgenstein’s </span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">Investigations</span><span style="color: black; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"> seems very to-the-point when it comes to the questions and difficulties I find myself coming up against here, and may help me plumb the depths of the matter: </span><br /><blockquote class="tr_bq"><span style="background-color: white; color: #222222; font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif; font-size: 11pt; white-space: pre-wrap;">So does it depend wholly on our grammar what will be called (logically) possible and what not,—i.e. what that grammar permits?”—But surely that is arbitrary!—Is it arbitrary?—It is not every sentence-like formation that we know how to do something with, not every technique has an application in our life [...].</span></blockquote>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com1tag:blogger.com,1999:blog-8137988136860941398.post-87477364020317428702017-03-14T16:02:00.000-07:002017-03-14T16:02:05.089-07:00Quantification and 'Extra Constant' Semantics<div class="tr_bq"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(The following&nbsp;is a companion piece to&nbsp;<a href="http://www.philpercs.com/2015/08/tarskian-satisfaction-is-stupid.html">this offsite post</a>.)</span></div><div class="tr_bq"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div class="tr_bq"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">In a fascinating new paper entitled '<a href="http://www-personal.usyd.edu.au/~njjsmith/papers/SmithTruthSatisfaction.pdf">Truth via Satisfaction?</a>', N.J.J. Smith argues that the Tarskian style of semantics for first-order logic (hereafter 'FOL'), which employs the special notion of satisfaction by numbered sequences of objects, does not provide an explication of the classical notion of truth - the notion of saying it like it is - but that the second-most prominent style of semantics for FOL, which works by considering what you get if you introduce a new constant, does. I agree with him about the first claim but disagree with him about the second.</span></div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">My main point in this post, however, is not to argue that Smith's preferred style of semantics for FOL fails to explicate the classical notion of truth. I will do that a bit at the end - although not in a very fundamental way - but the main point will be to draw out a moral about how we should think about the 'extra constant' semantics for FOL, and more generally, about how we need to be careful in certain philosophical contexts to distinguish mathematical relations (such as 'appearing in an ordered-pair with') from genuinely semantic ones (such as 'refers to'). The failure to do this, in fact, is what made Tarski introduce his convoluted satisfaction apparatus which others have muddle-headedly praised as some sort of great insight. (I blogged about this debacle, to this day largely unrecognized as such by the logical community,&nbsp;<a href="http://www.philpercs.com/2015/08/tarskian-satisfaction-is-stupid.html">offsite</a>&nbsp;in 2015.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">By way of intuitive explanation of the universal quantifier clause of his preferred semantics for FOL, Smith writes:&nbsp;</span><br /><blockquote class="tr_bq"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Consider a name that nothing currently has—say (for the sake of example) ‘Rumpelstiltskin’. Then for ‘Everyone in the room was born in Tasmania’ to say it how it is is for ‘Rumpelstiltskin was born in Tasmania’ to say it how it is—no matter who in the room we name ‘Rumpelstiltskin’. (p. 8 in author-archived version).</span></blockquote><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But this kind of explanation is not generally correct. Get a bunch of things with no names and stick them in a room. Now, doesn’t this purported explication of what it is for quantified claims to be true run, in the case of the claim ‘Everything in this room is unnamed’, as follows: for ‘Everything in this room is unnamed’ to say it how it is is for ‘Rumpelstiltskin is unnamed’ to say it how it is--no matter what in the room we name ‘Rumpelstiltskin’? And this, I think, is very clearly false; by hypothesis, everything in the room in question is unnamed, so surely ‘Everything in this room is unnamed’ says it how it is. But if we name one of the things in the room‘Rumpelstiltskin’, then ‘Rumpelstiltskin is unnamed’ will certainly not say it how it is.</span><br /><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Now, as Smith pointed out to me in correspondence, this problem with unnamedness can be avoided by considering another method of singling out objects, such as attaching a red dot to them. (The worry arises that some objects are abstract and so it makes no sense to talk about attaching a red dot to them, but I won't pursue that here.) Then you can use a slightly different form of explanation, and say that for 'Everything in the room is unnamed' to say it how it is is for 'The thing with the red dot on it is unnamed' to say it how it is no matter which thing in the room has the red dot on it. Now we will of course get a counterexample involving 'red-dotlessness' but we can then just consider a different singling-out device.</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">But this slightly different style of explanation is also not generally viable, as becomes clear when we consider, not unnamedness, but unreferred-to-ness. Things which haven't been named but have been referred to, say by a definite description, count as unnamed but not as unreferred-to. And let's stipulate that we are talking only about singular reference - so that even if 'All the unreferred-to things' in some sense refers to the unreferred-to things, it doesn't singularly refer to them, so this wouldn't stop them from being unreferred-to in the relevant sense.<br /><br />Now, applying the new style of explanation involving an arbitrary singling-out method to the case of 'Everything in this room is unreferred-to', we get:</span></div><blockquote><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">For 'Everything in this room is unreferred-to' to say how it is is for 'The thing with the red dot on it is unreferred-to' to say how it is, no matter which thing we put the red dot on.</span></blockquote><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">And this is wrong, not because the thing has a red dot on it, but because 'The thing with the red dot on it is unreferred-to' can't be true, whereas the quantified claim can be.</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">No analogous problem arises in the formal setting. If we specify that 'G' is to be mapped to the set of things in some room and 'F' is to be mapped to the set of unreferred-to things, and consider '(<span style="background-color: white; color: #242729; font-size: 15px;">∀</span>x)(Gx&nbsp;<span style="background-color: white; color: #242729; font-size: 15px;">⊃</span>&nbsp;Fx)', then neither Smith's preferred style of semantics for FOL nor the silly Tarskian style cause any sort of problem, since for there to exist a function which maps some constant&nbsp;<i>c</i>&nbsp;to an object&nbsp;<i>o</i>&nbsp;is compatible with&nbsp;<i>o</i>&nbsp;being unreferred-to. Thus we get the desired truth-value for '(<span style="background-color: white; color: #242729; font-size: 15px;">∀</span>x)(Gx&nbsp;<span style="background-color: white; color: #242729; font-size: 15px;">⊃</span>&nbsp;Fx)'.</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(You might now think: OK, but what if we replace unreferred-to-ness with not-being-mapped-to-by-any-function, or whatever? Don't we then get the wrong truth-value? Well, no, because - at least on a classical conception of functions - nothing&nbsp;<i>is</i>&nbsp;unmapped-to-by-any-function.)</span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span></div><div><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">So, quantified propositions are not correctly explicated by talking about the truth-values of propositions you get by naming things. Nor are they correctly explicated by adopting a non-semantic singling-out device and then considering propositions which talk about 'The thing' singled out. This in itself shouldn't really be news, but also noteworthy is that, despite such explications being incorrect, the style of semantics for FOL which works via consideration of an extra constant gives no undesired results, and is arguably better than the Tarski-style semantics, which is needlessly complicated and is born of philosophical confusion. (Still, it does create a danger that students of it will wrongly think that you&nbsp;<i>can&nbsp;</i>explain quantified propositions in the way shown here to be incorrect.)</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">What does this mean for Smith's claim that 'extra constant' style semantics for FOL explicates the classical conception of truth, the conception of saying it like it is? Well, I think that's an interestingly wrong idea anyway, and probably deeper things should be said about it, but: Smith's incorrect informal gloss of the formal quantification clause - which gloss, as we have seen, cannot be corrected by moving to an arbitrary singling-out device and talking about 'The thing' singled out - certainly seems to be doing important argumentative work in his paper. His main claim, bereft of the spurious support of the informal gloss, is as far as I can see completely without support.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><i><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Many thanks to N.J.J. Smith for discussion.</span></i></div>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-85851245494369573892017-02-15T17:18:00.001-08:002017-03-02T16:05:00.921-08:00The Resurgence of Metaphysics as a Notational Convenience<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Reading Jessica Wilson's interesting new SEP entry on <a href="https://plato.stanford.edu/entries/determinate-determinables">Determinables and Determinates</a>, the following speculation occurred to me: the oft-remarked-upon resurgence of metaphysics heralded by the work of David Lewis, D.M. Armstrong and others was driven in part by cognitive resource limitations and practicalities of notation; putting things metaphysically often lightens our cognitive loads and makes thinking and writing more efficient in many philosophical situations.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Wilson's piece is dripping with metaphysical turns of phrase, but much of what she says could be re-expressed in a conceptual or linguistic key. I think this goes for a good deal of contemporary metaphysics. However, converting metaphysically-expressed ideas and claims into a conceptual or linguistic key may make them a bit fiddlier to think and express. And if you're doing hard philosophy and need to think and express a lot of things, this extra cost is going to pile up. Sometimes, having things in a conceptual or linguistic register may make things clearer, and sometimes it may be essential. But for many purposes the metaphysical register does fine, and often has the benefit of being less resource-hungry.</span><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><br /></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Yes, some metaphysics may not be capturable in conceptual or linguistic terms, and perhaps even in favourable cases the capturing will not be complete or perfect. And there are doubtless other important things going on behind the sociological phenomenon of the resurgence of metaphysics. But maybe this is part of the story.</span><br /><br /><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">UPDATE: B<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">randon Watson <span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">(<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">at the end of a post on <span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Fi<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">tch's para<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">d<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">o<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">x) </span></span></span></span></span></span><a href="http://branemrys.blogspot.com.au/2017/02/evening-note-for-wednesday-february-22.html">links</a> to this post, writing: <span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">'</span></span></span></span><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"><span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">I'm very interested, of course, in accounts of how philosophical scenes get transformed, how ideas transmogrify, and the like. This hypothesis for the rise of analytic metaphysics makes considerable amount of sense, and is probably true.'<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"> T<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">his is encouraging!</span></span></span></span></span></span><br /><div id="UMS_TOOLTIP" style="background: transparent none repeat scroll 0% 0%; cursor: pointer; left: -100000px; position: absolute; top: -100000px; z-index: 2147483647;"></div>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com5tag:blogger.com,1999:blog-8137988136860941398.post-91832601958650693272017-01-20T22:25:00.000-08:002017-01-20T23:07:50.293-08:00'Close Enough' Closer to the Truth About Counterfactuals<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;">Lewis would have liked to be able to say that a counterfactual A &gt; C is true iff the corresponding material conditional is true at all closest worlds. But his example of the inch long line seemed to show that sometimes there are no clos<i>est</i> worlds - you can get closer and closer without limit to being one inch long while still not becoming one inch long. Wanting to avoid the Limit Assumption - the assumption that you do hit a limit as you get closer to actuality, after which you cannot get closer except by reaching actuality - he plumped for a clever, but complicated and costly solution; requiring that no A &amp; ~C world is closer to actuality than any A &amp; C world. (In his (1981) he admitted that this is costly in terms of simplicity and intuitiveness.)<br /><br /> I think Lewis here was too hung up on the idea of <i>minimal</i> change to the actual world. Proposing instead that a counterfactual A &gt; C is true iff the corresponding material conditional is true at all close <i>enough</i>, or relevantly similar, worlds is a better way to avoid the Limit Assumption. (This theory might work for indicatives, too, but that's an especially vexed issue.) Why is this better?<br /><br /> (1) It lets you have a simpler, more intuitive form of account, with a set of worlds which are relevant.<br /><br />(2) This also lets you have nice things like <a href="http://sprachlogik.blogspot.com/2016/05/sufficient-conditions-for-some.html">these results</a> about when it's OK to use certain inference patterns.<br /><br />(3) It better handles what might be called 'categorical' or 'no matter what' conditionals like 'If you had seen a cat then you would have seen an animal', where this is intended in such a way that you could add 'definitely' or 'no matter what' after the 'then' without changing the truth-condition, and is generally a more flexible<span style="font-family: &quot;georgia&quot; , &quot;times new roman&quot; , serif;"> and hence </span>powerful account.<br /><br />(4) It lets you straightforwardly explain why 'If this person had been taller, they would have been only a tiny bit taller' and the like are not true. Lewis can do this at the cost of saying that here close similarity in height just isn't important, but this is a little awkward given his case against the Limit Assumption.<br /><br /> (Donald Nute long ago proposed a 'close enough' account as better than Lewis's (see references below), but it seems few people listened. Also, some of his reasons can be diffused by being clever and flexible about what matters for similarity, and he didn't have (2) above to offer, and maybe not (3) either.)<br /><br /> Why <i>wouldn't</i> you go this way? One reason I can think of is that it may seem like a regrettable move to a less definite, less informative form of account. After all, if I am told 'the tallest people will be given a prize' this seems more informative than 'everyone tall enough will be given a prize'. But in the present context, this is illusory. You need to build in so much contextual flexibility into Lewis's account to make it at all plausible that the indefiniteness there swallows up the apparent difference in informativeness. Either that, or you keep the edge in definiteness but at the cost of implausible truth-value verdicts. Minimal change, I suspect, is a good way of thinking about lots of counterfactuals, and maybe those were the ones on Lewis's mind - but I see no reason why the change would ever have to be so minimal that you need to abandon having a set of relevant worlds and move to Lewis's official 'no A &amp; ~C world closer than any A &amp; C world' account. For other counterfactuals, minimality seems not to the point at all. So it's good to have a more flexible 'close enough' style account for your general theory of counterfactuals (or conditionals in general).<br /><b><i><br /> References</i></b><br /><br />Lewis, David (1981). Ordering semantics and premise semantics for counterfactuals. <i>Journal of Philosophical Logic</i> 10 (2):217-234.<br /><br /> Nute, Donald (1975). Counterfactuals and the similarity of words. <i>Journal of Philosophy</i> 72 (21):773-778. (Title [sic]. As far as I know it's just a very unfortunate typo and it should be 'worlds'.) </span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0